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TIA Flashcards

1
Q

3 levels of risk appetites

A
  1. Risk averse
  2. Risk neutral
  3. Risk lovers
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2
Q

Define the “complete portfolio”

A

The entire portfolio of the investor, made up of risk free assets (F) and risky assets (P)

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3
Q

Describe the mean-variance (M-V) criterion

A

Portfolio A dominates Portfolio B if:

E(rA) ≥ E(rB) and σA ≤ σB

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4
Q

Definition of “indifference curves”

A

Curves that contain different portfolios that the investor is indifferent about (portfolios with equivalent utility levels).

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5
Q

Describe the “Capital Allocation Line”

A

Graph of the risk/ return levels of various investment options available to the investor, based on the distribution of the complete portfolio.

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6
Q

Advantages of a passive over an active approach to investing

A

significantly cheaper than an active strategy

Free rider benefit

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7
Q

Describe the “Capital Market Line”

A

CAL that uses the Market portfolio as the risky portfolio

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8
Q

2 categories of risk

A
  1. Market/ Systematic/ Nondiversifiable Risk: the risk that can not be diversified away
  2. Unique/ Firm-Specific/ Nonsystematic/ Diversifiable: the portion of the risk that can be eliminated via diversification
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9
Q

Describe “Efficient Diversification”

A

A portfolio with the lowest risk level for a given return

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10
Q

Explain the separation principle

A

There are 2 steps to portfolio selection:

  1. Selection of the optimal risky portfolio
  2. Allocation between risk free vs risky assets
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11
Q

2 problems with the Markowitz model

A
  1. As the number of securities increases, the number of variables that need to be calculated increases dramatically
  2. Due to the large number of required estimates, it is likely that some variables are estimated incorrectly
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12
Q

Briefly describe the “single index model”

A

Version of the single-factor model, where the return on an index is used as a proxy for the common factor

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13
Q

Advantage of the single index model

A

To use the model in practice, significantly less estimates are needed than the number needed for the Markowitz model

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14
Q

Disadvantage of the single index model

A

Oversimplifies the true uncertainty

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15
Q

List some financial variables that may impact the level of Beta:

A
  • Firm Size
  • Debt Ratio
  • Variance of earnings
  • Variance of cash flow
  • Growth in earnings per share
  • Market capitalization
  • Dividend yield
  • Debt to asset ratio
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16
Q

List the 2 requirements to reject hypothesis that the alpha of the SCL is 0:

A
  1. the magnitude of alpha would need to be large enough for it to be deemed economically significant.
  2. alpha would also need to be statistically significant.
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17
Q

Steps required to derive the Optimal Risky Portfolio:

A
  1. Calculate the ratio of each security of the active portfolio
  2. Scale the above weights so total will equal 1
  3. Calculate the alpha, beta & residual variance of the active portfolio
  4. Calculate the weight of the active portfolio
  5. Calculate the weights of the market and each security in the optimal portfolio
  6. Calculate the risk premium and variance of the optimal portfolio
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18
Q

Briefly describe a key property of CAPM assumptions:

A

They should be robust: the predictions are not highly sensitive to a violation of the assumptions

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19
Q

2 key implications of CAPM:

A
  1. The market portfolio is efficient

2. The premium on a risky asset is proportional to its bet

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20
Q

List the 3 Individual Behavior assumptions:

A
  1. Investors are rational mean-variance optimizers
  2. Their planning horizon is a single period
  3. Investors use identical input lists (homogeneous expectations)
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21
Q

2 groups of CAPM assumptions:

A
  1. individual behavior

2. market structure

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22
Q

List the 4 Market Structure assumptions:

A
  1. All assets are publicly traded, and short positions are allowed. Investors can borrow/ lend at a common risk free rate.
  2. All information is publicly available
  3. No taxes
  4. No transaction costs
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23
Q

Describe where a fairly priced, underpriced & overpriced asset will lie relative to the SML:

A
  • Fairly priced: on the SML
  • Underpriced: above the SML
  • Overpriced: below the SML
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24
Q

3 reasons that short positions are not as easy to take as long positions:

A
  • There is no cap on the liability of short positions. A large short position will require significant collateral
  • There is a limited supply of stocks that can be borrowed by short sellers.
  • Many investment companies are prohibited from short sales. In addition, several countries restrict short sales.
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25
Q

Differences between the CML & SML:

A
  • CML: graphs risk premiums of efficient portfolios as a function of σ
  • SML: graphs risk premiums of individual assets as a function of β
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26
Q

2 examples of non traded assets:

A
  1. human capital

2. privately held businesses

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27
Q

Describe the impact to CAPM from privately held businesses that do not have similar characteristics to traded assets:

A

Owners of these businesses will bid up the prices of hedge assets, reducing their expected return. They will appear to have a negative α

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28
Q

Describe the impact to CAPM from privately held businesses that have similar characteristics to traded assets:

A

Little impact: owners of these businesses can still achieve diversification by avoiding similar traded assets

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29
Q

Describe the impact to CAPM from the human capital asset:

A

Since employees will avoid purchasing shares of their own employer, the shares of labor intensive firms will have lower demand, and therefore appear to have a positive α

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30
Q

2 adjustments that need to be made to CAPM to reflect liquidity:

A
  1. returns need to be increased if the stocks are illiquid

2. returns need to be increased if the stocks are subject to liquidity risk

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31
Q

What is a reasonable standard to apply to conclude that CAPM is the best available model to explain rates of return:

A

In the absence of security analysis, the expected value of alpha to be 0.

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32
Q

Explain why it does not make sense to require that all securities have an alpha of 0 in order to conclude that CAPM is the best available model to
explain rates of return:

A

This is not realistic: actions by security analysts are required in order to drive levels at which alpha is 0. However, if all
alphas were 0 anyway, there would be no point in conducting security analysis.

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33
Q

Briefly describe 2 ways to test a model:

A
  1. Normative: tests the assumptions of the model

2. Positive: examine the predictions of the model

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34
Q

Assuming that CAPM is the best available model, what steps should an investor take if she wants to outperform the market:

A

• Identify a practical index to use in the analysis
• Conduct macro analysis in order to forecast the index; and
securities analysis to identify the mispriced securities

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35
Q

List 2 predictions based on CAPM, that could be tested:

A
  1. The market portfolio is efficient

2. The SML accurately describes the risk-return trade off (α = 0)

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36
Q

Explain why tests of CAPM should focus on its robustness to assumptions:

A

CAPM assumptions are not completely accurate.
Simplifications are necessary due to the complexity of
the market.

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37
Q

List 2 reasons that CAPM may be used extensively in the market, despite its shortcomings:

A
  1. The decomposition of risk to systematic risk and firm specific risk is useful
  2. Evidence suggest that the main conclusion of CAPM (the efficiency of the market portfolio) is fairly accurate
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38
Q

Problem of testing the prediction that the market portfolio is efficient:

A

The market portfolio is unobservable

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39
Q

What is the implication of investors valuing additional income more during periods of tough economic times:

A

Assets that have a positive covariance with consumption growth (those that have a higher payoff when consumption is already high) are viewed as being riskier.

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40
Q

Upon what assumption is the Consumption Based CAPM based:

A

Investors need to allocate the current wealth between

consumption today; and savings/ investment to support future consumption.

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41
Q

2 disadvantages of CCAPM model:

A
  1. Consumption growth figures are published infrequently

2. Consumption growth figures are measured with significant error.

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42
Q

Describe a “factor portfolio”

A

A portfolio designed to have a β of 1 to the factor for which the risk premium is being measured, and a β of 0 to all other factors

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43
Q

Describe the “Law of One Price”

A

Two assets that are equivalent in all economically relevant aspects should have the same market price.

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44
Q

Describe an “Arbitrage Opportunity”

A

The opportunity to make a riskless profit without the need to make a net investment

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45
Q

Advantage of APT over CAPM

A

It does not require an all inclusive portfolio

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46
Q

3 assumptions of APT

A
  1. Security returns can be described by a factor model
  2. There are a sufficient number of securities to diversify away idiosyncratic risk
  3. Well functioning securities markets do not allow for the persistence of arbitrage opportunities
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47
Q

Difference between \Risk Return Dominance” & “Arbitrage” arguments:

A
  • Risk Return Dominance: many investors will make limited changes to their portfolios, depending on their degree of risk aversion. The culmination of the relatively small transactions of many investors produces sufficient volumes to move the market price.
  • Arbitrage argument: the investor who discovers the arbitrage opportunity will want to maximize his position in order to maximize profits.
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48
Q

Briefly describe the 3 versions of the EMH

A
  1. Weak form: stock prices reflect all information that can be derived from examining market data
  2. Semistrong form: stock prices reflect all publicly available information about the firms prospects
  3. Strong form: stock prices reflect all information relevant to the firm, including that not publicly available
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49
Q

What does the Efficient Market Hypothesis (EMH) state

A

Stock prices should reflect all available information

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50
Q

Describe “Fundamental Analysis”

A

Uses the fundamentals of a firm to determine the appropriate price.

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51
Q

Describe “Technical Analysis”

A

The search for predictable patterns of stock prices, which can be used to derive a profit from trading.

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52
Q

3 reasons why it is difficult to determine if the markets are truly efficient

A
  1. Magnitude Issue: the impact of the investment manager may be very small compared to the normal volatility of the market
  2. Selection Bias Issue: once an investment scheme becomes known by others, it will no longer generate abnormal returns.
  3. Lucky Event Issue: the number of investors is so large, just by chance, some have to make huge returns.
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53
Q

2 difficulties associated with conducting “event studies”, and how to deal with each

A
  1. the stock price may respond to a wide range of economic news in addition to the specific event: base the impact on the abnormal return
  2. information about the event may be leaked prior to the actual event: measure the \cumulative abnormal return”, starting at a point in time prior to the event.
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54
Q

Describe Semistrong Tests of EMH

A

Investigate whether publicly available information beyond the trading history can be used to generate abnormal returns

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55
Q

Examples of Weak-Form Tests of EMH

A
  • Returns over short horizons: Looks at whether investors can use historic trends to earn abnormal profits over the short term, by measuring the serial correlation of stock market returns
  • Returns over long horizons: Similar to the prior test, but looks at the long term returns
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56
Q

2 reason Efficient Market Anomalies are not necessarily a sign that the market is not efficient

A
  1. the properties are proxies for fundamental determinants of risk
  2. the properties arise just due to data mining
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57
Q

Examples of efficient market anomalies

A
  • Small-Firm-in-January Effect: small firms have historically generated superior returns, particularly in January.
  • Book-to-Market Ratios: High Book-to-Market firms have historically outperformed the rest of the market.
  • Post-Earnings-Announcement Price Drift: The cumulative abnormal return of stocks has been shown to continue to increase even after the information about the event becomes public.
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58
Q

Three uses of portfolio management, even if markets are efficient

A
  1. Diversification: selects a diversification strategy to eliminate firm-specific risk
  2. Reflects tax considerations of the individual investor
  3. Adjusts portfolio to reflect the unique risk profile of the investor
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59
Q

4 biases that cause information processing errors

A
  1. Forecasting Errors: too much weight is assigned to recent experience/ forecasts are too extreme given the actual level of uncertainty
  2. Overconfidence: Many investors overestimate their abilities.
  3. Conservatism: Investors are too slow to update their beliefs in response to new evidence.
  4. Sample Size Neglect & Representativeness: Investors do not account for sample size, and therefore may infer a pattern based on too small a sample.
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60
Q

Briefly describe the 2 categories of irrationalities

A
  1. Investors do not always process information correctly, and therefore derive incorrect probability distributions
  2. Investors often make inconsistent/ suboptimal decisions due to their behavioral biases
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61
Q

Factors that limit the actions of arbitrageurs

A
  • Fundamental Risk: Their actions are actually not risk free, because the mispricings are not necessarily going to disappear.
  • Implementation Costs: Arbitrageurs usually need to rely on short selling in order to exploit overpricing. There are often limitations to short selling
  • Model Risk: It is possible that the prices are indeed valid. Instead, there may be issues with the arbitrageurs model that are causing it to falsely indicate a mispricing
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62
Q

List 5 examples of Behavioral biases

A
  1. Framing: Decisions are often materially impacted by how the question is framed
  2. Mental Accounting: Investors may segregate decisions. Rationally, it would be better to optimize the risk-return
    profile of the entire portfolio in aggregate.
  3. Regret Avoidance: Investors who make decisions that turn out badly have more regret if it were an unconventional decision.
  4. Affect: paying more for a stock due to the good feeling associated with the company (that practices socially responsible practices)
  5. Prospect Theory: This modifies the standard financial theorys definition of risk averse investors.
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63
Q

List 3 criticisms of Behavioral Finance

A
  1. The behavioral approach is too unstructured: it allows virtually any anomaly to be explained by a combination of irrationalities.
  2. Some anomalies are inconsistent in their support for one irrationality vs another.
  3. Selecting the wrong benchmark can produce an apparent abnormality
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64
Q

List 2 examples where the Law of One Price has been violated

A
  1. Siamese Twin Companies

2. Equity Carve-outs

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65
Q

List 3 diagnostics used by technical analysts to measure market sentiment

A
  1. Trin statistic
  2. Confidence Index
  3. Put/Call Ratio
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66
Q

Briefly describe 3 approaches that try to profit from trends

A
  1. Moving Averages: If the market breaks through the moving average line from below, this is a bullish signal, as it is a sign of a shift from a falling trend to a rising trend.
  2. Relative Strength: Quantifies how the stock has performed relative to a benchmark. Look for a stock that is improving
  3. Breadth: This measures how widely the movement in the market index is reflected in the price movements of all stocks.
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67
Q

Define “Callable bonds”

A

Bonds that are issued with call provisions that allow the insurer to repurchase the bond at a specific call price before the maturity date.

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68
Q

2 types of Treasury bonds:

A
  • Treasury notes: original maturity between 1 to 10 years

* Treasury bonds: original maturity between 10 to 30 years

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69
Q

Define ”Deferred callable bonds”:

A

Similar to callable bonds, except that these have an initial period of call protection

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70
Q

Disadvantage of Callable bonds to the bondholders:

A

Issuers will typically repurchase the bonds if the interest rates fall, as they can replace them with new bonds that have lower coupons (refunding) This is disadvantageous to the bondholders as they potentially will have to forfeit the bond at a favorable time.

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71
Q

Define a “Convertible bond”:

A

Provide the bondholder the option to exchange the bond for a specified number of shares of the issuing firm

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72
Q

Define a ”Put bond”:

A

Similar to a callable bond, but gives the option to “retire” the bond to the bondholder.

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73
Q

Define ”Market conversion value”

A

Current value of shares for which the bond can be exchanged

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74
Q

Define “Conversion ratio”:

A

Number of shares that each bond can be exchanged for

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75
Q

Explain why floating rate bonds have less interest rate risk:

A

As interest rates rise, the increase in interest offsets the higher discounting rate.

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76
Q

Define ”Conversion premium”:

A

Excess of bond value over its conversion value

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77
Q

Describe the 2 categories of International bonds:

A
  • Foreign bonds: issued by a borrower from a country other than the one where the bond is sold. It is denominated in the currency of the country in which it is marketed
  • Eurobonds: denominated in one currency (usually that of the country of the issuer), but sold in other markets (for example a USD denominated bond sold outside the US).
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78
Q

Why do Inverse floaters depreciate significantly when the rates rise

A
  • The coupon level falls

* Each coupon is discounted by a greater magnitude

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79
Q

Define “Indexed bonds”:

A

Bonds that make payments that are based on a general price index, or the price of a specific commodity.

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80
Q

Define ”Yield to Maturity”:

A

Interest rate that produces a PV of bond payments equal to its price. This is the average return that the investor would earn if he purchases the bond now and holds it till maturity.

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81
Q

Relationship between coupon, current yield & YTM for premium bonds:

A

Coupon > current yield > yield to maturity

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82
Q

Define “current yield”:

A

Annual Coupon/Bond Price

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83
Q

List examples of determinants of bond safety:

A
  • Coverage ratio
  • Liquidity ratio
  • Leverage ratio
  • Profitability ratio
  • Cash flow to debt ratio
  • Altman Z score
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84
Q

2 offsetting risks that bondholders are exposed to when interest rates change:

A
  1. Bond prices will fall (price risk)

2. Reinvested coupon income would grow (reinvestment risk)

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85
Q

List 2 examples of coverage ratios:

A
  1. Times interest earned ratio = ratio of earnings before interest payments and taxes to interest obligations
  2. Fixed charge coverage ratio = ratio of earnings to all fixed cash obligations
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86
Q

Coverage ratios

A

= Ratio of company earnings to fixed costs.

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87
Q

2 examples of Liquidity ratios:

A
  • Current ratio = current assets/current liabilities

* Quick ratio = current assets excluding inventories/current liabilities

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88
Q

Leverage ratio =

A

Ratio of debt to equity. If this is too high, the firm may be unable to satisfy its obligations.

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89
Q

List restrictions imposed by Bond Indentures:

A
  • Sinking Funds
  • Subordination of Further Debt
  • Dividend Restrictions
  • Collateral
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90
Q

2 examples of Profitability ratios:

A
  1. Return on assets = earnings before interest & taxes/total assets
  2. Return on equity = net income/equity
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91
Q

Describe what subordination clauses do:

A
  • restrict the amount of additional borrowing

* require that the additional debt may be subordinated in priority to existing debt.

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92
Q

Definition of “short rate”

A

Interest that applies during a future time interval

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93
Q

Definition of “spot rate”

A

Interest that applies from time 0 to time t

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94
Q

Definition of ”forward rate”

A

Rate expected to apply during a future time period

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95
Q

List the 2 theories that can explain the shape of the yield curve

A
  1. Expectations Hypothesis

2. Liquidity Preference

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96
Q

Terminal value of an amount “A” that is invested for “n” years at a rate “R” continuously compounded, is

A

Ae^(Rn)

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97
Q

Describe the “Liquidity Preference Theory”

A

Bond investors would ideally select a bond which matures around the time that they need the money. They will require a premium to purchase a bond with a different maturity.
Therefore the shape of the yield curve will be influenced by the proportions of the different term investors.

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98
Q

Describe the “Expectations Hypothesis”

A

Forward rate equals the expected future short rate

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99
Q

Equation for Modified duration

A

D∗ = D/(1 + y)

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100
Q

Equation for Macaulays duration

A

D = Σtwt Where: wt = [CFt/(1 + y)^t]/Σ[CFt/(1 + y)^t]

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101
Q

The equation showing the relationship between the change in bond prices, convexity & duration

A

∆P/P = −(D∗)∆y + 0.5Convexity(∆y)^2

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102
Q

The equation that shows the relationship between the change in bond prices & duration

A

∆P/P = −(D∗)∆y

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103
Q

Equation for Effective Duration

A

Effective duration = −( ∆P/P )/∆r

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104
Q

Equation for convexity if rates are compounded “k” times per annum:

A

Convexity = [1/P(1+y/k)^2]Σ(CFtn*(n+1)/[(k^2∗(1+y/k)^n]

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105
Q

List the 2 types of interest rate risk to which an insurer is exposed, which immunization can help protect against

A
  1. price risk

2. reinvestment rate risk

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106
Q

How can an insurer achieve immunization

A

Set the duration of a portfolio equal to the investment horizon

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107
Q

Briefly describe 2 alternatives to immunization

A
  1. Cash Flow Matching: buy a zero which will make a payment that exactly matches the future cash obligation.
  2. Dedication Strategy: this is cash flow matching over multiple periods. Purchase a combination of coupon paying bonds and/ or zeros to match a series of obligations.
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108
Q

List some problems with immunization

A

• It is based on a measure of duration that makes the
assumption that the yield curve is flat. If this is not the
case, each cash flow needs to be discounted at its respective spot rate
• Immunizing the portfolio is only effective for parallel shifts in the yield curve
• Immunization is inappropriate in an inflationary
environment

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109
Q

Disadvantage of Cash Flow Matching/ Dedication Strategy:

A

hard to implement because they impose strong constraints on the bonds that can be selected.

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110
Q

2 advantages of Cash Flow Matching/ Dedication Strategy:

A
  1. automatically immunizes the portfolio from changing interest rates
  2. rebalancing will not be necessary
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111
Q

Reason that market makers usually need to participate in swaps:

A

It is unlikely that two parties will simultaneously contact a financial institution to take opposite positions in exactly the same swap.

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112
Q

Interest rate parity relationship (between US and UK as an example):

A

F1 = E0*(1+rUS)/(1+rUK) ; Where F1 and E0 are expressed in USD per pound

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113
Q

The profit to the Eurodollar contract buyer:

A

FT − F0 = (100 − LIBORT ) − (100 − contract rate) = contract rate − LIBORT

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114
Q

List a reason to purchase a credit default swap (CDS):

A

Bondholders may purchase CDS in order to transfer their credit risk exposure to the swap seller.

115
Q

Equation for net income

A

Net income = P - L - E + (S + P - E) * y

116
Q

Describe the “franchise value”

A

The economic value of the profits that will be earned in the future years from the future renewals of the current policies

117
Q

Equation for current economic value

A

C = S + P - E - L/ (1 + y)

118
Q

Equation for premium

A

P = [S (k - y) + L] / (1 + y) + E

119
Q

Equation for total economic value

A

Total economic value = C + F

120
Q

Equation for Franchise Value

A

F = [P - E - L/ (1 + y)] * d / (1 - d)

Where d = cr/ (1 + y)

121
Q

2 components of the practical dilemma that is caused by franchise value

A
  1. The greater the franchise value of the firm, the more difficult it is to manage the interest rate risk
  2. Reducing the duration of invested assets to offset the positive contribution of franchise value to the duration may puzzle regulators, as they only see the accounting numbers, and therefore do not account for the franchise value
122
Q

1 disadvantage of managing the duration via pricing policy

A

The desired combination of target return on surplus and target duration can be maintained only for small interest rate changes

123
Q

1 advantage of managing the duration via pricing policy

A

Avoids rating agency and regulatory risk that are associated with managing the duration of the invested assets

124
Q

Briefly describe the 3 types of triggers that would generate a payment from a CAT bond

A
  1. Indemnity triggers: the payouts are based on the sponsoring insurers actual losses.
  2. Index triggers: the payouts are based on an index of industry losses
  3. Hybrid triggers: these blend more than one trigger.
125
Q

List examples of risk linked securities

A
  • CAT bonds
  • Sidecars
  • Catastrophic Equity Puts
  • Catastrophe Risk Swaps
  • Industry Loss Warranties
126
Q

What trade off is made when selecting a trigger

A

Between moral hazard & basis risk

127
Q

Briefly describe the 3 types of index triggers

A
  1. industry loss indices: the estimated losses to the industry from an event
  2. modeled loss indices: runs the parameters of the event through a model of a catastrophe-modeling firm to generate losses
  3. parametric indices: triggered by specified physical measures of an event
128
Q

Who is most concerned about basis risk?

What is the appropriate trigger to protect against this?

A

Sponsor; Indemnity

129
Q

Who is most concerned about moral hazard?

What is the appropriate trigger to protect against this?

A

Investors; Industry Loss Index

130
Q

List 2 disadvantages to the insurer of using an Indemnity trigger

A
  1. may need to reveal confidential info

2. may require more time to reach a settlement due to length of loss adjustment process

131
Q

Disadvantage to insurer of using the Industry Loss index trigger

A

Higher basis risk

132
Q

2 reasons the high layers of exposure are often uninsured

A
  1. The credit risk of the reinsurer is a major concern in events of this magnitude.
  2. The highest layers usually have the highest reinsurance profit margins.
133
Q

List 2 disadvantages to the investor of using an Indemnity trigger

A
  1. potential for moral hazard

2. needs to obtain info on the sponsors portfolio

134
Q

Describe a “sidecar”

A

SPVs formed by insurers or reinsurers to provide additional capacity to write reinsurance

135
Q

List 3 reasons why Cat bonds are superior to reinsurance when insuring the high layers of exposure

A
  1. CAT bonds are fully collateralized, so credit risk is not a concern
  2. Investors are willing to accept lower spreads from CAT bonds because they offer diversification benefits
  3. multi year bonds are available, sheltering the sponsor from the cyclical price fluctuations of the reinsurance market
136
Q

Briefly describe how a Cat-E-Put works

A

The insurer purchases the Put from the writer, and receives the right to issue preferred stock to the writer at a specified price on the occurrence of a specified event.

137
Q

2 advantages of a ”sidecar” structure

A
  1. transactions are usually off-balance sheet, and therefore can be used to improve the reinsurers leverage
  2. can be formed quickly with minimal documentation/ admin costs
138
Q

2 disadvantages of a Cat-E-Put

A
  1. not collateralized, so exposes the insurer to credit risk

2. if the insurer issues preferred stock, the value of the existing shares will be diluted

139
Q

2 advantages of a Cat-E-Put

A
  1. the insurer will be able to raise equity after a catastrophe, when its stock price is likely to be depressed.
  2. lower transaction costs than CAT bonds, as no need to form a SPR.
140
Q

3 disadvantages of a Catastrophe risk swap

A
  1. it is difficult to create a swap that achieves parity
  2. can create more exposure to basis risk that some other types of contracts
  3. not prefunded
141
Q

2 advantages of a Catastrophe risk swap

A
  1. the (re)insurer reduces some of its core risk, and achieves diversification
  2. lower transaction costs than some of the other securities
142
Q

Briefly describe the 2 categories of payments that can be made by an ILW

A
  1. binary trigger: full payment is made once both triggers are satisfied
  2. pro rata trigger: payoff depends on the magnitude by which the loss exceeds the warranty
143
Q

Briefly describe the dual triggers of a ILW

A
  • retention trigger: based on the incurred loss of the insurer
  • warranty trigger: based on an industry wide loss index
144
Q

2 alternative methods of increasing the chance the a CAT bond will receive reinsurance treatment

A
  1. base the payment on narrowly defined geographic indices.

2. dual-trigger contracts (where the insurer can not collect more than its net loss)

145
Q

List 3 factors that could potentially threaten the growth of the risk linked securities market

A
  1. regulatory issues
  2. accounting issues
  3. tax issues
146
Q

Equation for EVAOC

A

EV AOCi = Net Income i/Ci − ri

147
Q

Equation for EVA

A

EV Ai = Net Income i − ri*Ci

148
Q

3 reasons that RBC shouldn’t be used to allocate capital

A
  1. The factors used in the derivation of the RBC are of
    questionable accuracy
  2. The calculations are often based on book value instead of market
  3. RBC ignores several important sources of risk
149
Q

3 examples of friction costs

A
  1. Agency & Informational costs: management may behave opportunistically, and therefore fail to achieve the owner’s objective of value maximization
  2. Double taxation
  3. Regulations may force the insurer to hold inefficient
    investment portfolios
150
Q

3 reasons that VaR shouldn’t be used to allocate capital

A
  1. The firm may not have enough capital to achieve a certain exceedence probability
  2. This does not consider the impact of diversification
  3. This does not reflect the amount by which losses will exceed the resources in the event that the exceedence level is breached.
151
Q

3 criteria that the RBC method needs to satisfy to ensure equity for all parties:

A
  1. The standard needs to be the same for all types of insurers
  2. The RBC needs to be objectively determined
  3. The approach should be able to distinguish between items that differ materially in level of riskiness
152
Q

List 4 alternate measures of income that can be used in the RAROC calculation

A
  1. GAAP Net Income: calculated using GAAP accounting
  2. Statutory Net Income: calculated using Statutory
    accounting rules
  3. IASB Fair Value: based on Fair value accounting
  4. Economic Profit: the change in \economic value” of the firm over a period
153
Q

Equation for RAROC

A

RAROC = Income/Risk-Adjusted Capital

154
Q

List 6 alternate measures of capital

A
  1. Actual Committed Capital: The actual capital provided by the shareholders
  2. Market Value of Equity: The market capitalization
  3. Regulatory Required Capital
  4. Rating Agency Required Capital: the amount of capital necessary to achieve a specific credit rating.
  5. Economic Capital: the amount of capital necessary to provide the firm with a certain probability of achieving a specific objective over the time horizon.
  6. Risk Capital: the amount of capital that needs to be
    provided by the shareholders to cover the risk that the
    liabilities may exceed the funds already provided
155
Q

List 3 problems with the \Economic Profit” measure

A
  1. ignores franchise value
  2. may make less sense to management, as the economic values often do not reconcile to GAAP accounting
  3. management may have difficulty justifying their decisions to external parties, as these parties only have access to statutory & GAAP accounting
156
Q

3 ways to derive the thresholds that are used to compare to the risk measures

A
  1. Bond default probabilities at a Selected Credit Rating Level: maintain enough capital that would result in a probability of default of the firm equal to the probability of default of a bond with a specific credit rating.
  2. Managements risk preferences: a threshold based on the risk tolerance of management.
  3. Arbitrary default probability: an arbitrary percentile that is relatively easy to measure.
157
Q

2 different objectives that can be used to derive the amount of Economic capital

A
  1. Solvency Objective: that the firm can meet its existing obligations to policyholders
  2. Capital Adequacy Objective: that the firm can continue to pay dividends/ grow premiums/ maintain a certain financial strength
158
Q

3 points to keep in mind if using bond default probabilities:

A
  1. Historical vs Current estimates: historical default rates are more stable, but current market estimates of default rates better reflect current conditions
  2. Different sources of default statistics may indicate different numbers, possibly because they use data from different periods
  3. Time Horizon: tables often provide annual default
    probabilities. However, risk capital models are often based on default during the lifetime of the liabilities
159
Q

2 disadvantages of using bond default probabilities as a threshold for the risk measure

A
  1. does not address which credit rating should be targeted

2. does not account for the risk of downgrade

160
Q

5 main categories of risk to which an insurer is exposed

A
  1. Market risk
  2. Credit Risk
  3. Insurance Underwriting Risk
  4. Operational Risk
  5. Strategic Risk
161
Q

4 disadvantages of using managements risk preferences as a threshold for the risk measure:

A
  1. will be difficult to get management to articulate and agree on a threshold
  2. the preferences of managers will often differ to the
    preferences of directors and shareholders
  3. this does not factor in risk, which is an important
    consideration to compare to reward
  4. managers will likely be focused on a number of issues that concern policyholders, and it may be hard to isolate the estimate of the threshold to just the probability of default
162
Q

3 reasons that the insurers credit risk exposure to reinsurance recoveries is unique

A
  1. definition of “default”: if the reinsurers credit rating gets downgraded below an investment grade level, it could enter a ”death spiral” where its policyholders try to end their contracts, resulting in severe liquidity problems
  2. substantial contingent exposure: the reinsurance recoverable at a given point in time may increase in the future due to adverse loss development
  3. reinsurance credit risk is highly correlated with the
    underlying insurance risk
163
Q

3 sources of exposure to credit risk to the insurer

A
  1. Marketable Securities/ Derivatives/ Swap Positions
  2. Insureds Contingent Premiums & Deductibles Receivable
  3. Reinsurance Recoveries
164
Q

Describe the 3 components of total risk that impact Loss Reserve Risk:

A
  1. Process Risk: risk that actual results will deviate from their expected value due to the random variation inherent in the claim development process
  2. Parameter Risk: risk that the actual expected value of the liability differs from the actuarys estimate of the expected value due to inaccurate parameters
  3. Model Risk: risk that the actual expected value of the liability differs from the actuarys estimate of the expected value due to the use of the wrong model
165
Q

3 categories of insurance underwriting risk

A
  1. Loss reserves on prior policy years: potential adverse
    development
  2. Underwriting Risk for the current policy year
  3. Property catastrophe risk
166
Q

5 advantages of Frequency & Severity Models over Loss Ratio Distribution Models:

A
  1. It is easier to account for growth in the volume of business
  2. Inflation can be more accurately reflected
  3. Changes in limit and deductibles can be more easily reflected
  4. The impact of deductibles on frequency can be accounted for
  5. The treatment of the split of loss between insured, insurer & reinsurer can be mutually consistent
167
Q

List 3 methods that can be used to quantify the Underwriting Risk:

A
  1. Loss Ratio Distribution Model
  2. Frequency & Severity Model
  3. Inference from Reserve Risk Models
168
Q

3 reasons that historical catastrophe losses are not the best measure of potential future losses:

A
  1. Events are rare
  2. Exposures change over time
  3. Severities change over time due to changes in the building materials & designs
169
Q

List 4 methods that can be used to derive the aggregate distribution from the Frequency & Severity distributions:

A
  1. Analytical Solution: generated based on the frequency & severity parameters
  2. Numerical Method: numerical approximation
  3. Approximation: based on the mean, variance (and possibly higher moments) of the collective risk model
  4. Simulation
170
Q

3 methods to quantify the dependency between risks

A
  1. Empirical Analysis of Historical Data
  2. Subjective Estimates
  3. Explicit Factor Models: These link the variability of the risks to common factors
171
Q

List the 3 components (modules) of Catastrophe models:

A
  1. Stochastic Module/ Hazard Module: generate the events
    that can occur, including the location, intensity, etc
  2. Damage (Vulnerability) Module: Derives the damage that would arise from an event, based on exposure information
  3. Financial Analysis Module: Applies the insurance/
    reinsurance terms to the losses to determine the financial impact to the insurer
172
Q

2 advantages of using Subjective estimates to quantify dependency between risks

A
  1. can account for the tail events

2. reflects the users intuition

173
Q

2 disadvantages of using Empirical analysis to quantify dependency between risks

A
  1. usually there is insufficient data to calculate the historical dependency
  2. there is little insight as to how the dependencies will change during tail events
174
Q

List 4 techniques to aggregate the distributions of the different risks

A
  1. Closed Form Solutions
  2. Approximation Methods: Eg assume that all of the
    individual distributions are normal or lognormal, and then derive the parameters of the aggregate
  3. Simulation Methods
  4. Square Root Rule (described in Goldfarb)
175
Q

1 disadvantage of using Subjective estimates to quantify dependency between risks

A

As the number of risk categories increases, the number of dependency parameters that need to be estimated increases exponentially.

176
Q

List the available methods to allocate capital

A
  1. proportional allocation based on a risk measure
  2. incremental allocation
  3. marginal allocation (Myers-Read)
  4. co-measures approach
177
Q

Equation for Economic Profit

A

EP = Prem - Expenses - Discounted losses + Investment return

178
Q

List 5 applications of risk adjusted performance metrics:

A
  1. Assessing capital adequacy
  2. Setting Risk management priorities
  3. Evaluating alternative Risk Management strategies
  4. Risk adjusted performance measurement
  5. Insurance policy pricing
179
Q

Briefly describe the inconsistent time horizons that firms use when assessing the aggregate risk profile:

A
  • Market risk is often based on a one year period

* Insurance risks are based on the ultimate liability

180
Q

List some problems with looking at the Insurance risks over only 1 year:

A
  • There is little available methods/ data to estimate the timing of the recognition of adverse loss development
  • The change in value perspective for loss reserves will not be totally consistent with market risk, as it will most likely focus on the best estimate of the reserve.
  • The information that would result in the revaluation of the liabilities is often not available over the short term, and as a result, there will likely be minimal change in the liability valuation, despite potential significant risk over the long term.
181
Q

Problem with quantifying the Market Risk over a longer term period:

A

It is much more difficult to derive the parameters. Also the investment strategy is likely to change in response to market movements

182
Q

List 3 examples of the deteriorating quality of mortgages in the last decade:

A
  1. Ratio of mortgage values to home prices increased
  2. Increased use of second lien loans
  3. Increased issuance of mortgages with low/ no documentation
183
Q

Why does systematic risk make up such a large portion of the overall risk of structured products:

A

Because structured products pool together the risk from several assets, the non systematic risk is usually diversified away

184
Q

List 4 characteristics of CMOs that are biases against the investors:

A
  1. Higher probability of default due to lower credit quality of borrowers.
  2. Lower recovery values, because when the assets do need to be sold, they are often sold under financial pressure.
  3. High level of default correlation due to pooling mortgages from similar geographic areas/ vintages.
  4. Due to the CDO2 structure, the impact of errors in the estimates is magnified.
185
Q

What is the alternate interpretation of the 99th percentile capital requirement that Bodoff provides:

A

The firm holds enough capital even for the 99th percentile loss.
The key difference between this and the prior definition is that this also considers losses at lower percentiles.

186
Q

Bodoff’s interpretation of the statement that investors demand that the insurer hold capital based on the VaR (Value at Risk) at the 99th percentile:

A

The firm holds capital to pay for the loss level at the 99th percentile, but not for loss events that are greater or less than this level: capital is allocated only to the components that contribute to this particular scenario.

187
Q

2 reasons that a loss would receive a higher allocation in the upper layers than in the lower layers:

A
  1. There are a fewer events that pierce the layer

2. The layer of capital is wider because the incremental increase to severity of each event tends to increase in size.

188
Q

Describe the Horizontal procedure of capital allocation:

A

Allocate each layer of capital to the loss events that penetrate the layer.

189
Q

Describe the Vertical procedure of capital allocation:

A

Allocates capital to each loss event based upon the layers that it penetrates

190
Q

Advantages of capital allocation by percentile layer:

A
  • Allocates capital to the entire range of loss events (rather than just the most extreme events)
  • Tends to allocate more capital to events that are more likely
  • Tends to allocate significantly more capital to events that are more severe
  • Eliminates the need to select an arbitrary percentile level to use as a basis for allocating capital, as it is based on all relevant percentile thresholds
  • Always allocates 100% of the capital
  • Provides a method to allocate capital by layer
191
Q

Disadvantage of using Profit to rate an insurer, compared to using Rate of Return

A

It is difficult to use “Profit” to compare companies if we don’t have other information

192
Q

2 ways to measure profit of an insurer

A
  1. Profit

2. Rate of Return

193
Q

Describe “opportunity cost”

A

Since the policyholder pays premiums before the losses are paid by the insurer, the policyholder is losing potential investment income.

194
Q

3 examples of bases that can be used in the Rate of Return calculations

A
  1. Equity
  2. Assets
  3. Sales
195
Q

What discount rate should the opportunity cost be calculated at? Why?

A

Risk free rate: the policyholder is not exposed to insurer’s investment risk

196
Q

2 factors impacting opportunity cost

A
  1. line of business

2. infrastructure investment

197
Q

2 reasons that policyholders should only get credit for investment income from policyholder funds

A
  1. shareholder funds do not belong to them

2. including shareholder funds will penalize high surplus insurers

198
Q

2 components of insurer’s investment earnings

A
  1. investment income from policyholder funds

2. investment income from shareholder funds

199
Q

2 advantages of using ROS

A
  1. understandable

2. does not require surplus allocation

200
Q

2 problems of using ROE to regulate an insurer

A
  1. forces regulator to focus on ROE instead of rate equity

2. surplus needs to be allocated

201
Q

3 examples of changes to structure of industry if rates are inadequate

A
  1. increasing size of residual market
  2. Reducing degree of product diversity
  3. Reduced innovation
202
Q

List & briefly describe the 2 markets of insurance transactions

A

Financial Market
• transactions between shareholders & insurer
• return to shareholders depends on the risk of investment
Products Market
• transactions between policyholders & insurer
• premium depends on the supply/ demand of insurance

203
Q

3 problems of using fixed Profit Margin when pricing insurance policies

A
  1. Lack of theoretical justification of the fixed margin
  2. High interest rates suggest the fixed margins may be too low
  3. Doesnt reflect increasing competitiveness of the insurance industry
204
Q

Describe how companies use IRR to decide whether to undertake an investment.

A

If IRR >Opportunity Cost, project should be profitable

205
Q

What is the difference between “IRR” and “Opportunity Cost”

A
  • IRR: rate which sets the NPV of cash flows to zero.

* Opportunity Cost: the investment return that the providers of capital could earn from an alternate investment

206
Q

2 situations when NPV and IRR may give different conclusions

A
  1. Projects with unusual cash flows
  2. Projects with budget constraints/ Mutually exclusive
    projects
207
Q

List 2 assumptions for timing of surplus commitments/ release that an insurer can make

A
  1. surplus is committed once a policy is written, and no longer needed when it expires
  2. surplus is committed when UEPR is established, and declines as losses are paid
208
Q

Reason that IRR can be used for expected cash flows, whereas NPV should be used for actual cash flows

A

Expected cash flows do not usually have sign reversals, but actuals may.

209
Q

Problem of IRR for projects with unusual cash flows

A

If cash flow patterns change between inflow and outflow more than once, there may be two positive roots to the IRR

210
Q

2 reasons that insurers reinvestment rate is usually equal to the IRR

A
  1. If a pricing model produces an IRR which is greater than the cost of capital, insurers can use this extra revenue to write more policies
  2. Policies are usually priced using an underwriting profit provision which sets the IRR equal to the cost of capital.
211
Q

Reason that IRR and NPV analyses may give different results for mutually exclusive projects

A

The IRR analysis assumes that the revenues are reinvested at the IRR, which isnt necessarily true.

212
Q

Why are insurers more likely than other companies to have positive IRRs less than the cost of capital

A

Deteriorating results are usually associated with an increase in reserves. This increase in reserves results in increasing investment income, which offsets the poor underwriting results.

213
Q

List a practical criticism of the IRR

A

If IRR >0, but less than the Cost of Capital, regulators may get the false impression that the insurer is profitable

214
Q

When deriving surplus required, some insurers do not distinguish between policy form. Give an example of a type of policy that will therefore have overstated surplus required

A

Retro

215
Q

7 risks that surplus is meant to protect against

A
  1. Asset risk: chance assets will depreciate
  2. Pricing risk: chance that losses & expenses are ultimately greater than initially expected
  3. Reserving risk: risk that reserves are insufficient
  4. Asset-liability risk: changes in interest rates will affect the market value of assets differently to liabilities
  5. Catastrophe risk
  6. Reinsurance risk: risk that reinsurance recoverables wont be collected
  7. Credit risk: risk that agents/insureds wont remit premium
216
Q

When deriving surplus required, some insurers rely only on true insurance risk. Give an example of a type of policy that will therefore have understated surplus required

A

Retro/ Excess/ LDD

217
Q

When deriving surplus required, some insurers do not distinguish between policy form. Give an example of a type of policy that will therefore have understated surplus required

A

Excess

218
Q

List 2 differences between fixed assets of a manufacturer & surplus of an insurer

A
  1. A manufacturer can objectively measure the needed assets, whereas the needed surplus is an estimate based on expected future development.
  2. A manufacturer can divide the assets into product, but surplus cannot be divided into line.
219
Q

What 3 types of ROR does Ferraris equation link

A
  • ROE (T/S)
  • ROA (I/A)
  • ROS (U/P)
220
Q

Equation for “insurance exposure”

A

P/S

221
Q

List the parties interested in each of the ROR measures linked in Ferraris equation

A
  • ROE: Investors
  • ROA: Society
  • ROS: Regulators
222
Q

How does “leverage” arise for an insurer

A

Policyholders pay premiums before they receive a return from the insurer

223
Q

Equation for “insurance leverage factor”

A

1 + R/S

224
Q

In the equation T/S = A/I + R/S*(A/I + U/R), how can “UR” be interpreted

A

“Interest cost” incurred by the firm to use the reserves

225
Q

How can an insurer use Ferraris equations to decide whether to keep writing business

A

In T/S = I/A+ R/S*( A/I + U/R ), if the term in brackets is negative, the insurer should stop writing

226
Q

What impact does writing more business have on the Capital Structure

A

Increases liabilities relative to owners equity

227
Q

Describe “Optimum Capital Structure”

A

Mix of Owners Equity & Liabilities that maximizes the value of the firm.

228
Q

Describe 2 ways writing more business changes firm value

A
  1. increases earning stream, increasing value

2. increases volatility, increasing discount rate, reducing value

229
Q

Two factors which affect the value of the firm (and direction of impact)

A
  1. Expected earnings stream (increase)

2. Rate at which this stream is discounted by the market (decrease)

230
Q

According to Balcarek, 3 relationships ignored by Ferrari

A
  1. increase in P/S results in reduction to I/A
  2. increase in U/P results in increase in P/S
  3. increase in U/P results in increase in I/A
231
Q

Complication in relationship between increased writings and resulting discount rate

A

Increased writings usually results in increased diversification, which reduces volatility and therefore discount rate

232
Q

Briefly describe the 5 types of underwriting profit provision that Robbin refers to:

A
  1. Provision included in manual rates/ filings to change manual rates
  2. Corporate target underwriting profit provision: this should be sufficient to generate an expected return similar to that provided by investments with similar risk
  3. Breakeven underwriting profit provision: these provide a rate of return to stockholders equal to the rate of return on risk free investments.
  4. Charged underwriting profit provision: the rate achieved after applying experience and schedule rating modifications, as well as other adjustments
  5. Actual underwriting profit: these will differ from the charged provisions
233
Q

3 problems with the guideline that an underwriting provision is adequate if it produces an adequate profit:

A
  1. It is not obvious how to apply it in ratemaking
  2. There is a question of what is an adequate total return
  3. Ratemaking is conducted on a prospective policy year basis, but total return is measured on a calendar year basis
234
Q

3 advantages of the CY Investment Income Offset Procedure

A
  1. Data is easily obtained and verified
  2. Since the figures are reported in filed documents, it is less likely that the insurer is making pessimistic projections in order to increase the profit provision
  3. The calendar year investment portfolio yields are relatively stable
235
Q

Equation for Adjusted Underwriting Profit Provision under CY Investment Income Offset Procedure

A

U = U0 − iAF IT ∗ P HSF

236
Q

2 components of PHSF

A
  1. PHSF on UEPR

2. PHSF on Loss Reserves

237
Q

Disadvantage of the CY Investment Income Offset Procedure

A

Since CY results are retrospective, they may not be totally applicable to prospective ratemaking

238
Q

Ratio of “PHSF on Loss Reserves” to “Earned Premium”

A

(Loss Reserves: Loss Incurred) * PLR

239
Q

Ratio of “PHSF on UEPR” to “Earned Premium”

A

[UEPR(1 - Prepaid expense %) - Premium Receivable] / EP

240
Q

2 disadvantages of the CY Investment Income Offset Procedure

A
  1. Lack of economic theory supporting the calculation

2. Distorted if large change in volume or reserve adequacy

241
Q

2 advantages of the CY Investment Income Offset Procedure

A
  1. Data easily obtained

2. Short & straight forward calculation

242
Q

3 advantages of Present Value Offset Method

A
  1. Accounts for investment income in a simple manner
  2. Not distorted by rapid growth / decline
  3. No need to select target return or allocate surplus
243
Q

How does the “Present Value Offset Method” determine the Profit Provision

A

Calculates an Investment Offset to the traditional provision that is based on the difference of PVs of the line being priced, and a short tailed reference line

244
Q

In the “PV Cash Flow Return Model”, to what point in time are the cash flows discounted?

A

Start of the first year

245
Q

How does the “PV Cash Flow Return Model” determine the Profit Provision

A

Produce a PV of total cash flow (discounted at investment ROR) equal to the PV of changes in equity (discounted at target ROR).

246
Q

How is Investment Income derived in the Cash Flow Return Method

A

Based on surplus

247
Q

In PV Cash Flow Return Model, Cash Flow =

A

Underwriting Cash Flow + Investment Income - Tax

248
Q

Disadvantage of Cash Flow Return Method

A

Not clear what type of profit is being measured, as cash flows do not have the same timing as GAAP income

249
Q

Advantage of Cash Flow Return Method

A

PV of Cash Flows is how most people think about underwriting profits

250
Q

In the “Risk Adjusted DCF Model”, to what point in time are the Cash Flows discounted?

A

End of first year

251
Q

How does the “Risk Adjusted DCF Model” determine the Profit Provision

A

Calculates a fair premium, and then derives a provision
from that Fair premium =Risk adjusted present value of
underwriting cash flows + present value of taxes.

252
Q

3 advantages of the Risk Adjusted DCF Model

A
  1. Great intuitive appeal
  2. Grounded in modern financial theory
  3. Not necessary to determine a target ROR
253
Q

How is Investment Income derived in the Risk Adjusted DCF Model

A

Based on surplus

254
Q

5 examples of Model Construction Questions

A
  1. Should surplus be included in the model?
  2. How should the surplus requirement be determined?
  3. How should risk be incorporated into the model?
  4. It is better to use cash flows or incomes flows?
  5. How to reflect income taxes?
255
Q

Disadvantage of the Risk Adjusted DCF Model

A

Hard to determine beta

256
Q

2 examples of Parameter Selection Questions

A
  1. What discount rate should be used?

2. What is the right target return?

257
Q

Equation for Underwriting Profit Provision in terms of CR

A

U = 1 - CR

258
Q

Equation for Combined Ratio, as presented by Robbin

A

CR = VR + [(1+c)L + FX]/P

259
Q

According to Robbin, 2 ways in which profit provisions can be regulated

A
  1. Rate of return approach: rates should be regulated to ensure that companies are able to achieve an adequate return.
  2. Constrained free market theory: the premiums will move to an optimal level via market forces
260
Q

Equation for underwriting income during the jth accounting period:

A 
Uj = EPj − ILj − IXj
Where:
U = Underwriting Gain
EP = Earned Premium
IL = Incurred Loss
IX = Incurred Underwriting & General Expense
261
Q

List 2 goals that Robbin has for prices:

A
  • Should be consistent & sensitive to risk. These models will satisfy this, as the rate of returns are sensitive to the impact of leverage (as will be demonstrated later).
  • Should reflect managements risk return preferences. To achieve this, the model is based on the theoretical amount of surplus as opposed to the actual level.
262
Q

Equation for assets in the single period model:

A 
Aj = UEPRj + XRSVj + LRSVj + Sj
Where:
UEPR = Unearned Premium
XRSV = Statutory Expense Reserve
LRSV = Loss Reserve
263
Q

Equation to derive Qj (required GAAP equity) from Sj (required surplus):

A

Q0 = S0 + DAC
Qj = Sj; forj = 1; 2; :::; n
Where: DAC = Deferred acquisition costs (this will fall to 0 after a year)

264
Q

Equation to derive the IRR on Equity Flows:

A

ΣF j × (1 + y)^−j = 0

265
Q

Equation for Equity Flow:

A

F0 = I0 − Q0 = −Q0; SinceI0 = 0
For j = 1; 2; :::; n;
Fj = Ij − (Qj − Qj − 1) = Ij − ∆Qj − 1

266
Q

List an advantage of the PVI/PVE method over the IRR approach:

A

It uses a market based rate as the reinvestment rate

267
Q

List one issue with the IRR method:

A

Makes the assumption that the cash flows are reinvested at the IRR, which may differ from the market rate.

268
Q

3 major distinctions of the RA DCF models:

A
  1. doesnt require the user to select a target return
  2. The RA DCF model is not based on a particular accounting structure. It therefore has no way to reflect the conservative treatment of expenses in SAP accounting, nor can it reflect reserve discounting.
  3. Surplus does not have a large impact on premium in this method
269
Q

2 approaches to derive the risk adjusted rate:

A
  1. View the adjustment as a form of compensation to the insurer for placing its capital at risk in the insurance contract
  2. Use CAPM
270
Q

List the desirable qualities for an allocatable risk load formula:

A
  • It can be able to be allocated down to any level
  • The risk load of any sum of random variables should equal the sum of the risk loads allocated individually
  • The same additive formula can be used to calculate the risk load for any subgroup or group of groups
271
Q

Managements desired properties of the riskiness leverage ratio:

A
  • Be a down side measure
  • Be roughly constant for excess that is small compared to capital
  • Become much larger for excess that significantly impacts capital
  • Reduces to 0 (or at least doesnt increase) for excess that significantly exceeds capital
272
Q

List some source of risk that may call for a generic management risk load:

A

Risk of not making plan/ Risk of serious deviation from plan/Risk of not meeting the investor analysts expectations/ Risk of a downgrade from the rating agencies/ Risk of triggering a regulatory notice/ Risk of going into receivership/ Risk of not getting a bonus

273
Q

Regulators preferences for the riskiness leverage:

A
  • Be 0 until the capital is seriously impacted

* Not decrease (for excess that significantly exceeds capital) because of the risk to the state guaranty fund

274
Q

Equation for Risk Load in Marginal Surplus method

A

Risk Load = Multiplier * Marginal SD

275
Q

Equation for Multiplier in the Marginal Variance method

A

yz(1+y)/[SD(L+n)]

276
Q

Equation for Multiplier in the Marginal Surplus method

A

yz/(1+y)

277
Q

Which of the methods discussed by Mango are renewal additive

A

Shapely Value/ Covariance Share

278
Q

Define “renewal additivity”

A

The sum of renewal risk loads of each risk is equal to the risk load for the aggregate portfolio.

279
Q

Explain why the Marginal Variance method is not renewal additive

A

It double counts the covariance, and therefore overstates the risk load in renewal

280
Q

Explain why the Marginal Surplus method is not renewal additive:

A

The square root function is sub additive, and therefore

understates the risk load in renewal

281
Q

4 features of “cooperative games with transferable utilities”:

A
  1. Participants that have benefits or costs to share
  2. Opportunity to share the benefits/ costs due to the
    cooperation of all (or a subgroup of) the participants
  3. Ability of the players to enter into negotiations
  4. Conflicting player objectives, where each wants to maximize his/ her share of the benefits (or minimize the share of the costs)
282
Q

Explain how the Marginal Variance, Shapely Value and Covariance Share methods allocate the mutual covariance upon renewal

A
  • Covariance: allocates the entire mutual covariance to each account
  • Shapely: allocates an equal amount of the covariance to each account
  • Covariance Share: allocates a user specified portion of the covariance to each account
283
Q

Factors to consider when deciding how much to allocate to a member of the group

A
  • Stability/ incentive to split from the group
  • Bargaining power
  • Marginal impact to the group’s characteristic function value
284
Q

Difference between a sub-additive and super-additive characteristic function:

A
  • Sub-additive: Σv(Xi) > v (Xi elements in unison)

* Super-additive: Σv(Xi) < v (Xi elements in unison)

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