Review Flashcards
IIA Open End MF are traded at
Closed End MF are traded at
Open: NAV
Closed: sold at the prevailing market price; must sell shares thru broker
IIA
* publicly traded limited partnership
* limited partners provide capital, general partners
manage activities
* approximately 90% of cash flow must come from
investments in real estate, commodities, or natural
resources
MLP master limited partnership
IIA Investors’ Choice Fund had NAV per share of $37.25 on January 1, 2009. On December 31 of the same year the fund’s rate of return for the year was 17.3%. Income distributions were $1.14, and the fund had capital gain distributions of $1.35. Without considering taxes and transactions costs, what ending NAV would you calculate for Investors’ Choice?
.173 = (P - $37.25 + 1.14 + 1.35)/$37.25; P = $41.20
IIA
- are traded on a major exchange
* unsecured debt securities
* can be sold short or purchased on margin
* no coupon payments
* have a maturity date
ETNs
IIA
* may be public (trades on exchange) or private
* considered a form of UIT
* invests in real estate directly
* must distribute 90%+ of income to shareholders
* receives special tax treatment
* offers diversification, professional management, higher yields, tax
advantages, liquidity
REIT
IIB Size (Capitalization)
Value of a company
= share price X # of outstanding common shares
Style
Value: Market price is LOWER than fundamental valuation
Growth: higher
Book value
Defined
A valuation based on a company’s assets minus its
liabilities.
Formulae
Book Value = assets minus liabilities
Book Value Per Share
= (assets-liabilities) / shares outstanding
= shareholder equity / shares outstanding
Intrinsic Value vsMarket Price
- The intrinsic value (IV) is the “true” value,
according to a model. - The market value (MV) is the consensus value
of all market participants.
Volatility
Defensive: less susceptible to economic cycles/conditions (ie pharma, food, power, water, gas)
Dynamic: more susceptible
Current Ratio
current assets/current liabilities
Quick Ratio
[cash + cash equiv. + short-term investments + receivables] /
current liabilities
Cap Weighted Index
“Market value weighted index”
ex. S&P 500, Russell 2000, MSCI EAFE
this index weights individual
companies or stocks based on their market
capitalization thus larger stocks receive more
proportional representation in the index; the
value of a cap-weighted index may be
computed by summing the value of all market
capitalizations and dividing by the number of
stocks in the index
PEG Ratio
Price-Earnings-Growth Rate (PEG Ratio)
PEGR = (P/E) / EGR
This ratio employs the P/E ratio and relates it to a firm’s expected growth rate per year
(EGR). It reflects the firm’s potential value of a share of stock.
Suppose that a firm with a P/E of 8.72 expects an annual growth rate of 8%. Its PEGR
would be
=8.72/8 = 1.09
It is theorized that PEGRs represent the following:
If PEGR = 1 to 2: The firm’s stock is in the normal range of value.
If PEGR < 1: The firm’s stock is undervalued.
If PEGR > 2: The firm’s stock is overvalued.
Return on Assets
Defined
* ROA is a ratio that measures how well company management
is utilizing its assets to generate operating income. It is calculated by dividing earnings before interest and tax payments by total assets.
Example
* ROA = EBIT/assets or
= EBIT/(liabilities + owner equity + retained earnings)
Note: sometimes ROA may be defined as Net earnings
(i.e., after taxes and interest payments)/assets.
Return on Equity
Defined
ROE is a ratio that measures how well company management is
performing for shareholders (i.e., profitability). It is calculated
by dividing after-tax earnings by shareholder’s equity (i.e.,
book value). It can also be calculated by dividing earnings per share by book value per share.
ROE = net earnings/shareholder’s equity
= net earnings/book value
= earnings per share (aka EPS)/(book value per share)
Formula for P/B, P/E and ROE:
P/B = P/E * ROE
Retention Ratio
Example: Company has return on equity of 17%, earnings of $1.75 per share, and pays a dividend of $0.25 per share. The retention rate (i.e., amount used to keep
growing the company – and is not paid out to shareholders) is calculated as follows:
One method for calculating a company’s growth rate is to use something called a
retention rate (or ratio). You multiply the ROE x the retention rate. Retention rate is basically 1 minus the dividend rate paid out.
Example: Company has return on equity of 17%, earnings of $1.75 per share, and pays a dividend of $0.25 per share. The retention rate (i.e., amount used to keep
growing the company – and is not paid out to shareholders) is calculated as follows:
1 – (dividend/earnings)
1 – (0.25/1.75)
1 – .1429
Retention Rate = 85.71%
Growth = ROE x retention rate
= 17% x 85.71%
=14.57% (answer)
A firm has a P/E ratio of 12 and a ROE of 13%. What is the price-to-book value?
1.56
P/B = P/E * ROE
= 12 * 0.13
= 1.56
Note that the above formula is derived from the definitional formulas for the ratios: P/B (Price to Book), P/E (Price to Earnings) and ROE (Return on Equity).
Recall, the denominator in ROE is Equity, which is based on book value and NOT a stock’s market price. See CIMA textbook pages 426-433 for more detail about these ratios.
For the specific derivation of the formula:
P/E * ROE = [(Price/share) / (Earnings/share)] * [(Earnings/share) / (Book Value/share)]
= [(Price/share) / (Earnings/share)] * [(Earnings/share) / (Book Value/share)]
= [(Price/share)] * [ 1 / (Book Value/share)]
= (Price/share) / (Book Value/share)
= P/B
Reminder: the denominator of Equity in ROE is
= [(Price/share) / (Earnings/share)] * [(Earnings/share) / (Equity/share)]
= [(Price/share) / 1 ] * [ 1 / (Equity/share)]
= [(Price/share) / (Equity/share)]
= P/Eq
= P/B
A firm has an ROA of 14%, a debt/equity ratio of 0.8, a tax rate of 35%, and the interest rate on the debt is 10%. The firm’s ROE is ______________.
11.18%
ROE = (1-tax rate) X (ROA+ (ROA - interest)D/E Ratio)
ROE = (1 - 0.35)[14% + (14% - 10%)0.8] = 11.18%.
Bulldog Stock enjoyed earnings last year of $21,000,000 while holding $100,000,000 in assets and $10,000,000 in liabilities. Bulldog’s book value and return on equity last year were:
$90,000,000 and 23.3%
Book Value = assets minus liabilities = $100m - $10m = $90m
ROE = earnings / shareholder equity = $21m / $90m = 23.3%
Calculate the current and quick ratios, respectively, for IVY League stock.
Cash $10,000,000
Receivables $42,000,000
Inventories $35,000,000
Capital long-term investments $75,000,000
Property and equipment $225,000,000
Short-term accounts payable $27,000,000
Long-term debt $150,000,000
3.22, 1.93
Current Ratio = current assets divided by current liabilities.
Current Assets for this company = cash, receivables, inventories = $87m
Current Liabilities = short-term accounts payable = $27m
$87m / $27m = 3.22
Quick Ratio = (cash and equivalents + ST investments + receivables) / current liabilities
Quick Ratio assets for this company = cash, receivables = $52m
Current Liabilities = short-term accounts payable = $27m
$52m / $27m = 1.93
What is the CAPE ratio of the following stock?
Stock price $45.10/share
Forward looking PE ratio = 22.2
Current PE ratio = 31.6
Current earnings per share = $2.08
Inflation adjusted 10-year historical earnings per share = $1.12
40.27
Shiller PE Ratio
also known as the “cyclically adjusted (CAPE) PE”
smoothes out fluctuations in earnings due to the business cycle
uses earnings per share figures adjusted for inflation and averaged over 10 years as the denominator
CAPE Ratio formula:
share price / 10-year earnings average adjusted for inflation
$45.10 / $1.12 = 40.27
What is the PEG ratio of the following stock and determine whether it is over or undervalued?
Stock price = $60.00/share
Current PE ratio = 32
Current earnings per share: $1.87
Projected earnings per share: $1.96
6.65, overvalued
PEGR = P/E divided by expected growth rate
Solve for growth rate: ($1.96 - $1.87) / $1.87 = 4.81%
32 / 4.81 = 6.65
This ratio employs the P/E ratio and relates it to a firm’s expected growth rate per year (EGR). It reflects the firm’s potential value of a share of stock.
It is theorized that PEGRs represent the following:
If PEGR = 1 to 2: The firm’s stock is in the normal range of value.
If PEGR < 1: The firm’s stock is undervalued.
If PEGR > 2: The firm’s stock is overvalued.
Use the retention rate to determine growth rate for the following company.
ROA = 2.12
ROE = 3.57
EPS = $0.87
PE Ratio = 17.25
Dividends = $0.12
3.08%
Solve for retention rate: 1 – (dividend/earnings)
1 – (0.12 / 0.87) = 86.21%
Growth = ROE x retention rate
= 3.57 x 86.21% = 3.08%
Using Retention Ratio to solve for growth rate
One method for calculating a company’s growth rate is to use something called a retention rate (or ratio). You multiply the ROE x the retention rate. Retention rate is basically 1 minus the dividend rate paid out.
Another example: Company has return on equity of 17%, earnings of $1.75 per share, and pays a dividend of $0.25 per share. The retention rate (i.e., amount used to keep growing the company – and is not paid out to shareholders) is calculated as follows:
1 – (dividend/earnings)
1 – (0.25/1.75)
1 – .1429
Retention Rate = 85.71%
Growth = ROE x retention rate
= 17% x 85.71%
=14.57% (answer)
Which of the following statements concerning convexity are accurate or true?
I. A common use for convexity is to estimate the percentage price changes in bonds for assumed changes in time.
II. Convexity measures the curvature of the price/yield relationship.
III. Given its limitations, modified convexity is not ideal for analyzing securities with embedded options.
IV. Convexity is often described as the first-order approximation of price changes while duration represents a second derivative of price change.
II and III only
A common use for convexity is to estimate the percentage price changes in bonds for assumed changes in yield.
Convexity measures the curvature of the price/yield relationship.
Given its limitations, modified convexity is not ideal for analyzing securities with embedded options.
Duration is often described as the first-order approximation of price changes while convexity represents a second derivative of price change.
The duration of a perpetuity with a yield of 8% is:
1.08/0.08 = 13.50 years
You purchased an annual interest coupon bond one year ago with 6 years remaining to maturity at the time of purchase. The coupon interest rate is 10% and par value is $1,000. At the time you purchased the bond, the yield to maturity was 8%. If you sold the bond after receiving the first interest payment and the bond’s yield to maturity had changed to 7%, your annual total rate of return on holding the bond for that year would have been _________.
FV = 1000, PMT = 100, n = 6, i = 8, PV = 1092.46;
FV = 1000, PMT = 100, n = 5, i = 7, PV = 1123.01;
HPR = (1123.01 - 1092.46 + 100)/1092.46 =
11.95%.
A bond will sell at a discount when the coupon rate is ______than the current yield and the current yield is _____ than yield to maturity.
the coupon rate is less than the current yield and the current yield is less than yield to maturity.
In order for the investor to earn more than the current yield, the bond must be selling for a discount. Yield to maturity will be greater than current yield as investor will have purchased the bond at discount and will be receiving the coupon payments over the life of the bond.
What amount of loss should not be exceeded in a thirty-day period of time?
Assume the portfolio is valued at $6,000,000 and has a standard deviation of 18%. Use
a 99% confidence level.
a. $90,000
b. $614,790
c. $868,158
d. $1,080,000
Answer: c. $868,158
Solution: CIMA Section IV.B. Risk Measurements
VaR = [(portfolio value) x (SDEV) x ((square root of (value / days)) x confidence level]
VaR = [($6m) x (18%) x (square root of 30/252) x (2.33)]
VaR = [($6m) x (18%) x (.3450) x (2.33)]
VaR = $868,158
Remember the confidence levels: 95% = -1.65, 99% = -2.33
Remember there are 252 trading days in the year.
How much of a $1,000,000 portfolio is at risk this year, with 99% confidence
when the portfolio’s expected return is 11% and has a standard deviation of 13%.
a. $130,000
b. $192,900
c. $65,000
d. $90,909
Answer: b. $192,900
Solution: CIMA Section IV.B. Risk Measurements
VaR = - [(expected return) + (z-score x SDEV)] x portfolio value
VaR = - [(.11) + (-2.33 x .13)] x $1,000,000
VaR = .1929 x $1,000,000
VaR = $192,900
Remember the confidence levels: 95% = -1.65, 99% = -2.33
What is the beta of Asset A where the standard deviation of Asset A is
4.34% and the expected return is 7%. The market standard deviation is 5.78%
with an expected return of 9%. The covariance between the market and Asset
A is -16.98.
a. 3.91
b. -2.94
c. -0.51
d. 0.90
Answer: c. -0.51
Solution: -16.98 / 5.782 = -0.51 on formula sheet
What is the beta of Asset A where the standard deviation of Asset A is
4.34% and the expected return is 7%. The market standard deviation is 5.78%
with an expected return of 9%. The correlation between the market and Asset
A is -0.677.
a. 0.90
b. -0.38
c. -0.51
d. 0.53
Answer: c. -0.51
Solution: (-0.677 x 4.34) / 5.78 = -0.51 on formula sheet
You invest $7,200 in security A with a beta of 0.45 and $3,310 in
security B with a beta of 1.02. The beta of the resulting portfolio is:
a. 0.63
b. 0.74
c. 0.84
d. 1.47
Answer: a. 0.63
Solution:
Use the formula for beta of a portfolio on your CIMA exam formula sheet.
$7,200 + $3,310 = $10,510
$7,200 / $10,510 = 68.51%; $3,310 / $10,510 = 31.49%
0.6851(0.45) + 0.3149(1.02) = 0.6295
The monthly SDEV of portfolio A is 2.17. Annualized it is:
=7.5171
=2.17* Square Root of 12
Co-Efficient of Variation =
CV = SDEV/ mean
= the relative SDEV
Skewness negative vs positive
Negative: fewer but more extreme outcomes to the LEFT of the mean. SD may underestimate the risk
Positive: fewer but more extreme outcomes to the RIGHT of the mean. SD may overestimate the risk.
Correlation Coeff
indicates the degree of a relationship between 2 variables. Always lies between -1 and 1. 0 = lack of any linear relationship. negative = diversification. low positive is good all considering.
Substitute vs Complementary goods
similar goods that may satisfy consumer if prices rise (ex Pepsi vs Coke) VS
add value to consumer when used in tandem (fries & ketchup)
Keynes Vs. Monetarism
Keynes: govt intervention is necessary
Monetarism: limit role of govt; advocate for steady incr in money supply
Price Elasticity of Demand =
% change in quantity demanded / the % change in price
If the price of a product rises by 12% and the change in demand falls by 10%, what is the price elasticity?
-0.83 = -10%/12%
Leading Indicators
vs Coincident
vs Lagging
Leading: consumer confidence, manager’s purchasing index, bond yields, money supply, housing permits/starts
Coincident: personal income, industrial production, manufacturing sales
Lagging: unemployment, quantity of loans, CPI, consumer credit, ratio of inventories to sales
Comparitive vs. Absolute Advantage
comparative: the ability to produce goods/services for a lower opportunity cost than a competitor
absolute: ability to produce MORE goods/services than a competitor
What is the futures price of an asset if its current market price is $75, the discount rate is 8% and there is no cash flow or holding costs and the maturity is 6 months?
= $77.94
= 75 (1 + .08)^0.5
An american invests in a chinese stock that rises 12%. The Chinese Yuan declines 6% against the USD in that same period. What is the return in USD?
Adjusted return = (1+return in local currency)X(1+change in currency value) - 1
= (1.12)(1-.06)-1=
5.28%
Suppose a USD:CZK is 22.5 and increases to 22.99. The USD appreciated relative to CZK by ____%?
The CZK depreciated by ___% relative to USD?
22.99/22.50 - 1 = 2.22% USD:CZK
(1/22.99)/(1/22.50) = -2.173% CZK:USD
Last year, Tracy, a US investor, bought 1000 shares of a Chinese tech stock for 80 Yuan (RMB). The exchange rate at that time was $0.16 per RMD. The stock paid dividends during the year of 4.1 RMB/sh. Currently, the stock trades at 97 RMD/sh and the exchange rate is now $0.19 per RMB.
What is the return in USD?
50.07%
Find basis in USD, gain in USD.
R1+dividends-R0 / R0
19209-12800 / 12800
A 4.5% 10-year bond has a YTM of 5.0% and a duration of 7.50 years. If interest rates rise by 50 basis points, how will the value of the bond reflect such a change?
= -(7.50/1 + 0.05)*0.005
= -3.57%
What amount of loss should not be exceeded in a thirty day period of time? Assume the portfolio is valued at $6m and has a SDEV of 18%. Use a 99% confidence level.
$868,158
VaR= Port Value * SDEV * [ Sq root of (value/days) * confidence level]
2.33 for 99%
1.65 for 95%
How much of a $1,000,000 portfolio is at risk this year, with 99% confidence, when the
portfolio has an expected return of 11% and standard deviation of 13%?
= -$192,900
VaR = Vp * {E[R] – [z * σp * (Vd/Dy)1/2]}
= $1,000,000 * {0.11 – [2.33 * 0.13 * (252/252)½]}
= $1,000,000 * {0.11 – [2.33 * 0.13 * 1]}
= $1,000,000 * {-0.19292} = -$192,900
How to interpret this:
With 99% confidence we can say the portfolio will change in value no more than a loss
of $192,900.
With 99% confidence, we expect the portfolio to return no worse than
-192,900/$1,000,000 = -19.29%
But 1% of the time, the portfolio would be expected to lose at least $192,900. In other
words, VaR does not predict the worst possible outcome.
With a lower level of confidence of 95%, we would predict a smaller loss of
VaR = $1,000,000 * {0.11 – [1.65 * 0.13 * 1]} = -$104,500
Given a $12 million portfolio with an expected return of 0% and a standard deviation of 11%, what is the maximum loss expected with a 95% confidence level in a ten-day trading period (i.e., two weeks)?
VaR = Vp * {E[R] – [z * σp * (Vd/Dy)1/2]}
= $12,000,000 * {0 – [1.65 * 0.11 * (10/252)½]}
= $12,000,000 * {0 – [1.65 * 0.11 * 0.1992]}
= $12,000,000 * {0 – 0.0362} = -$434,400
How to interpret this:
The VaR for the two-week period is -$434,000 (or -3.62%).
95% of the time, portfolio value will change by no worse than -$434,000.
5% of the time, the portfolio is expected to change by -$434,000 or worse.
This method of calculating VaR is defined as the absolute VaR because it assumes that
the portfolio value will not change, which can be acceptable for periods of time.
A so-called “kink” in the Capital Allocation Line (CAL) best demonstrates:
when the rate to borrow exceeds the lending rate.
the efficient frontier when maximum leverage is used.
the optimal portfolio of risky assets.
the tangency line.
when the rate to borrow exceeds the lending rate.
The so-called “kink” in a Capital Allocation Line indicates that leverage is being used, and that the rate to borrow exceeds the lending rate.
disposition effect
The disposition effect describes scenarios in which investors typically hold onto losing investments too long but sell winning investments too early.
The tendency to hold onto losing investments too long can be tied back to the so-called “snake-bit effect” where investors are seeking to avoid losses.
The tendency to sell winners too early may be traced to an investor’s seeking to lock in a gain and in doing so either avoid the risk of losing said gain, and/or to experience the immediate gratification that comes from the realized gain.
Your client’s municipal bond portfolio is now worth $540,000. He originally invested $430,000 seven years ago (equals his cost basis). His marginal federal ordinary income tax rate is 40% and his state rate is 6%. Your client’s state exempts muni-bond interest but not realized gains from sales. The tax rate on long-term capital gains is currently 25%. He asks you to sell the entire portfolio to fund the purchase of a second home. What are the tax consequences for doing so?
$34,100
Municipal bond funds may generate some tax-free income but gains from the sale of the fund itself are taxable. In this case the gains are considered “long-term” capital gains as the fund shares have been held more than one year. The entire gain of $110,000 is taxed at 31% since the fact pattern specifically states that this state does not exempt realized gains from the sale of muni-bonds from its state income tax.
Your client, Sue, is happy with the returns in her portfolio. Her portfolio’s beginning balance was $476,507 and the balance at year’s end was $551,062. She made no contributions to, nor distributions from the account during that time. Over the past year, her portfolio had long-term recognized gains of $36,771; realized but unrecognized long-term gains of $22,800; and non-qualified dividends of $14,984. Sue pays 20% tax on capital gains and qualified income and 40% tax on ordinary income. What is Sue’s after-tax total return for last year?
12.84%
Sue’s before-tax return is 15.65% ($551,062 - $476,507 = 74,555/$476,507). Recognized long-term gains are taxed at 20%, leaving $29,416.80. Unrecognized gains of $22,800 are not currently taxed. Non-qualified dividends are taxed at 40%, leaving an after-tax gain of $8,990.40. After-tax gains total $61,207.20 /$476,507 = 12.84%.
Which of the following are accurate as they relate to technical analysis?
I. A golden cross describes when a short-term average crosses up and through a longer-term average.
II. A continuation pattern indicates a price trend is moving strongly toward/with its longer term trend.
III. A dead cross describes when a long-term average crosses down and through a shorter-term average.
IV. A corrective pattern indicates a price trend is moving against the larger or more important trend.
IV and I only
A golden cross describes when a short-term average crosses up and through a longer-term average.
A continuation pattern indicates a price trend is experiencing a temporary diversion from its longer-term trend.
A dead cross describes when a short-term average crosses down and through a longer-term average.
A corrective pattern indicates a price trend is moving against the larger or more important trend.
Which of the following investment strategies typically identifies the most clearly defined risk management techniques?
tactical asset allocation
market timing
strategic asset allocation
dynamic asset allocation
dynamic asset allocation
CIMA Section III.D. Tools and Strategies
Dynamic asset allocation offers defined risk management techniques such as constant proportion portfolio insurance.
You and the investment committee believe that emerging markets equities will outperform other equities over the next 3-5 years and that inflation and interest rates around the world will be stable with a bias toward lower rates. The investment policy statement allows for tactical shifts in allocations based on the committee’s and consultant’s analysis and conclusions. Which of the following activities would not be appropriate based on this information?
Increase emerging markets exposure and decrease bond allocations
Buy the BRIC index and sell U.S. and global ex-U.S. funds to raise the capital
Reduce U.S. stock holdings and increase exposure to emerging markets equities
Raise emerging markets equities while selling cash (money market funds)
Increase emerging markets exposure and decrease bond allocations
Assuming a tactical asset allocation protocol is appropriate and implemented, you might consider raising allocations to emerging markets (obviously) and raise the needed funds by selling cash, or reallocating away from other equities. Based on the information given, you would probably not make changes to your bond allocation or sell bonds to raise capital to fund your increase in exposure to emerging markets.
Which of the following most accurately describes arbitrage as it relates to investing strategies?
Transactions that produce profits for any given level of risk
Prices change while risk does not thus offering opportunities to gain.
Arbitrage opportunities often exist in fully developed, efficient markets.
Gains may be made by capitalizing on shifting risks.
Prices change while risk does not thus offering opportunities to gain.
CIMA Section IV.A. Risk
The definition of “arbitrage” is a set of transactions that produces riskless profits; hence, the price changes while risk does not. The gains are made based on price inconsistencies (or mispricing).
As diversification increases, the total variance of a portfolio approaches ____________.
1
0
the variance of the market portfolio
-1
the variance of the market portfolio
CIMA Section IV.B. Risk Measurements
As more and more securities are added to the portfolio, unsystematic risk decreases and most of the remaining risk is systematic, as measured by the variance of the market portfolio
Determine the separate upside and downside capture ratios, respectively, for the following fund based on the data given below.
Returns Year 1 Year 2 Year 3 Year 4
Benchmark Index +12% -20% +40% -5%
Fund Performance +15% -32% +56% -12%
134.58% and 176.60%
To calculate the upside capture ratio, the positive returns are geometrically compounded then annualized. Then the resulting return of the fund is divided by the resulting return of the benchmark. The downside capture ratio is calculated the same way except that only the returns in negative years are used.
Calculate the upside capture ratio:
Benchmark’s geometric mean for positive years = [(1+0.12)(1+0.40)]1/2 -1 = 25.2198%
Fund’s geometric mean for positive years = [(1+0.15)(1+0.56)]1/2 -1 = 33.9403%
Upside Capture Ratio = Fund’s geometric mean divided by Benchmark’s geometric mean
= 33.9403%/25.2198%
= 134.58% or 1.3458
Calculate the downside capture ratio:
Benchmark’s geometric mean for negative years = [(1+-.20)(1+-0.05)]1/2 -1 = -12.822%
Fund’s geometric mean for negative years = [(1+-0.32)(1+-0.12)]1/2 -1 = -22.6437%
Downside Capture Ratio = Fund’s geometric mean divided by Benchmark’s geometric mean
= -22.6473%/-12.822%
= 176.6% or 1.766
Suppose you held a well-diversified portfolio with a very large number of securities. If the standard deviation of your portfolio was 0.25 and standard deviation of the market was 0.21, the beta of the portfolio would be approximately ________.
1.19
CIMA Section IV.B. Risk Measurements
standard deviation of portfolio / standard deviation of the market = beta
beta = (0.25) / (0.21) = 1.19.
The key to this problem lies in the language that it’s a well-diversified portfolio with a large number of securities. As such, we can expect the portfolio to correlate closely with the market with a correlation coefficient of about 1.00.
So, when the question asks about the approximate value of beta, it’s referencing this assumed (high positive) correlation.
Note: A similar question has surfaced on the certification exam through the years, so it should not be surprising for you to see something like this on that test (i.e., where you have to draw the conclusion that beta is 1.00).
Using the historical data presented below, calculate the Sharpe Ratio of this portfolio.
2014 portfolio return = 8%; risk-free rate = 2%
2015 portfolio return = 7%; risk-free rate = 3%
2016 portfolio return = 9%; risk-free rate = 2%
2017 portfolio return = 5%; risk-free rate = 3%
CIMA Section IV.C. Performance Measurement and Attribution
Sharpe Ratio = (Rp-Rf)/SDEV
YR 1 = 8-2 = 6
YR 2 = 7-3 = 4
YR 3 = 9-2 = 7
YR 4 = 5-3 = 2
Numerator then = AVG. = 4.75 of those totals
SDEV of 6, 4, 7, and 2 = 1.9202 (using N here – but you might need to N-1 on the cert exam if using N does not yield an answer choice)
Denominator then = 1.9202
Sharpe Ratio = 4.75/1.9202 = 2.4737
Suppose you purchase one share of the stock of Cereal Correlation Company at the beginning of year 1 for $50. At the end of year 1, you receive a $1 dividend, and buy one more share for $72. At the end of year 2, you receive total dividends of $2 (i.e., $1 for each share), and sell the shares for $67.20 each. The time-weighted return on your investment is __________.
CIMA Section IV.C. Performance Measurement and Attribution
Time-Weighted Return refers to the geometric average return, weighting each time period equally (i.e., ignoring different amounts invested at different times). Thus, the return for each time period must be calculated:
Year 1: ($72 + $1 - $50)/$50 = 46%
Year 2: ($67.20 + $1 - $72)/$72 = -5.28% (return shown on a per share basis, could also be based on amounts invested that year)
Time-weighted average = [(1+0.46) * (1+ -0.0528)]1/2 -1 = 1.176 -1 = 0.1760 = 17.6%
Suppose you purchase one share of the stock at the beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend and buy one more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each share) and sell the shares for $36.45 each. The dollar-weighted return on your investment is _______.
12.35%
QUIZ Question #24 - IV.C.
The following data are available relating to the performance of Wildcat Fund and the market portfolio:
Wildcat Fund Market Portfolio Average Return 18% 15% Standard Deviation of Returns 25% 20% Beta 1.25 1.00 Residual Standard Deviation 2% 0%
The risk-free return during the sample period was 7%.
What is the information ratio measure of performance evaluation for Wildcat Fund?
50%
CIMA Section IV.C. Performance Measurement and Attribution
P = 18% - [7% +1.25(15% - 7%)] = 1%;
[Avg Return - CAPM = Rp-Rb]
2% = tracking error (residual SDEV)
P/(eP) = 1%/2% = 0.50, or 50.00%
Note: There are several possible ways to calculate information ratio (in practice). This solution used the CAPM to determine excess return (vs. simply subtracting the market return from the fund return) and used the residual standard deviation of the fund which was given (since the difference of the SDEV of fund and market was the same, given that SDEV of the market was zero).
Calculate the Sharpe Ratio for the following mutual fund:
Return Risk-free Rate
Year 1 17% 4.0%
Year 2 12% 3.5%
Year 3 8% 3.0%
Year 4 11% 3.5%
Year 5 7% 3.0%
1.93
3.49
3.12
2.41
2.41
CIMA Section IV.C. Performance Measurement and Attribution
Step 1: 17 – 4 = 13; 12 – 3.5 = 8.5; 8 – 3 = 5; 11 – 3.5 = 7.5; 7 – 3 = 4. Average real return = 7.60.
Step 2: Calculate SDEV (13, 8.5, 5, 7.5, 4) = 3.1528.
Step 3: Divide 7.60 by 3.1528 = 2.4106.
Here we used population (N) to get SDEV. But be ready to calculate using sample (n-1) just in case.
Which of the following statements are accurate?
I. According to the consultant’s graph, risk goes down over time due to diversification.
II. According to the consultant’s graph, returns are more variable over time due to diversification.
III. According to the Samuelson-Merton graph, terminal value has less predictability over time.
IV. According to the Samuelson-Merton graph, returns are more predictable over time.
II and IV only
I and III only
II and III only
I and IV only
I and III only
CIMA Section V.B. Client Discovery
TRUE - According to the consultant’s graph, risk goes down over time due to diversification.
FALSE - According to the consultant’s graph, returns are more variable over time due to diversification.
TRUE - According to the Samuelson-Merton graph, terminal value has less predictability over time.
FALSE - According to the Samuelson-Merton graph, returns are more predictable over time.
Given the recent turbulent financial markets, you begin offering your clients access to a balanced portfolio consisting of 20% long-term corporate bonds, 20% diversified stock funds, 20% real assets, 20% U.S. Treasury bonds, and 20% in a diversified currency fund. Often called an all-weather portfolio, this model identifies market types and risks and seeks to manage them most appropriately. This type of investing is also called:
I. dynamic asset allocation.
II. a Black-Litterman model.
III. risk parity investing.
IV. risk factor investing.
III and IV only
CIMA Section V.D. Portfolio Construction
Risk factor investing consists of identifying various risk factors and allocating investments based on expectations about risk, as compared with traditional asset allocation models which allocate investments based on asset classes or styles and/or risk-return optimization models.
Risk parity investing includes identifying risk factors and managing those risks instead of investing based on mean-variance and other optimization models. Risk parity often includes using leverage on lower risk assets to help counterbalance higher risk assets and boost returns.
Black-Litterman models allow one to overlay expectations about risk, return, and other factors onto existing allocation models.
Dynamic asset allocation often includes tactical shifts and/or market timing techniques, but it is also identified as a method for managing downside risk in traditional asset allocation models by making periodic adjustments to allocations based on gains and losses of each allocation.
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
CIMA Section V.D. Portfolio Construction
E(RP) = 0.43(10%) + 0.57(8%) = 8.86%
The logic behind how we construct the risk-free portfolio follows from the general philosophy of how to form a minimum variance portfolio.
What we’re looking for is the mix of assets A & B that provides the smallest variance or standard deviation.
In the case of two assets that are perfectly negatively correlated (i.e., Corr Coeff = -1), we know that the standard deviation of the minimum variance portfolio is zero. (See “Key Concepts,” Section V.D. Portfolio Construction Slide 24).
In other words, because these two assets are perfectly negatively correlated, we can combine A & B in the right mix such that there is no variance and a fixed return (i.e., risk-free return) is provided.
In general, the Standard Deviation of a portfolio of two assets A & B is shown by the formula:
SD(A,B) = Square Root of [(WA^2)(SD(A)^2)) + ([(WB^2)(SD(B)^2)) + 2(WA)(WB)Corr(A,B)SD(A)SD(B)]
…in which:
WA = Weight of portfolio in Asset A
WB = Weight of portfolio in Asset B
SD(A) = Standard Deviation of Asset A
SD(B) = Standard Deviation of Asset B
The text limitations of fonts here make this look much harder than it is. See the CIMA Formula Sheet, Second Page, Second Column for “Standard Deviation of Two Risky Assets.”
In this case we know that the Corr Coeff(A,B) = -1.
If you set the Standard Deviation equal to 0 (because a perfect hedge allows for a risk-free portfolio) and substitute -1 in for the Corr Coeff in that formula, you can then factor the equation and, since WA + WB = 100%, you can solve for the WA and WB.
What you find is that the risk-free portfolio occurs when WA = SD(B) / [SD(A) + SD(B)].
Thus, the minimum risk portfolio occurs when the weight of Asset A is based on the ratio of the Standard Deviation of Asset B divided by the sum of their Standard Deviations. And visa-versa.
Once you know the weights of each asset in the portfolio, then the portfolio return is the weighted averaged of the returns of each of the assets.
Solution: E(RP) = 0.43(10%) + 0.57(8%) = 8.86%
Using the data below, calculate the total value created by this manager’s overall active management, and whether she added more value through market timing or asset selection.
Asset Class Fund Weight Fund Return Target Weight Benchmark Return
Cash 5% 1.89% 5% 1.22%
Bonds 20% 2.24% 35% 3.01%
Stocks 75% 19.19% 60% 16.20%
4.10%, market timing
2.12%, market timing
4.10%, asset selection
2.12%, asset selection
Use the formula from the CIMA Formula Sheet.
Calculate the value added for active management: sum (actual weight x actual return) – sum (target weight x benchmark return):
= [(.05 x 0.0189) + (.20 x 0.0224) + (.75 x 0.1919)] – [(.05 x 0.0122) + (.35 x 0.0301) + (.60 x 0.1620)]
= 0.1494 – 0.1083
= +0.0410
Thus, the manager added 4.1% in value from engaging in active management since the result of the calculation is greater than zero.
Next, calculate the value added for active asset allocation (“timing”):
cash = (0.05 - 0.05) * 0.0122 = 0.0000
bonds = (0.20 - 0.35) * 0.0301 = -0.0045
stocks = (0.75 - 0.60) * 0.1620 =+0.0243
add them all up = +0.0198 value added from timing
Next, calculate the value added for active asset selection:
cash = (0.0189 - 0.0122) * 0.05 = +0.0003
bonds = (0.0224 - 0.0301) * 0.20 = -0.0015
stocks = (0.1919 - 0.1620) * 0.75 = +0.0224
add them all up = +0.0212 value added from asset selection
Thus, this manager added slightly more value through asset selection. Note - using these formulae from IWI’s CIMA Formula Sheet, the value added by the two components (timing and selection) do not always add up to equal the exact value of the active management. This is due to unexplained variables.
That being said, these differences are usually relatively small in such calculations. So, if the net value (positive or negative) from those two components does not equal the exact amount of value added from overall active management, that’s ok for testing purposes.
Lastly, students often report that some form of attribution analysis is tested on the CIMA cert-exam. You may have to calculate value from overall active management or calculate the value from timing or asset selection. But it’s been a long time since students reported having to do the entire set of calculations like you were asked to do above.
From the following data, choose the manager with the most impressive skill as represented by the information ratio. The annual market return over this period was 10% and the risk-free rate was 4%.
Fund A Fund B Fund C Annual Return 12% 15% 9% Residual Standard Deviation 15% 18% 11% Beta 1.1 1.5 1.25 Excess Return 2% 5% -1%
Information Ratio is the average excess return of a portfolio over a benchmark divided by the standard deviation of excess returns. This measures the ability to select securities relative to a benchmark. It captures both the size of the excess return and the ability to do so consistently. “Math for Investment Consultants”
Information Ratio is calculated by dividing excess return (or alpha) by tracking error.
Remember that you are looking for the fund manager with the “highest” information ratio as that should indicate which of the managers is likely demonstrating more skill (rather than luck).
Note: Based on the data given, you might have to calculate alpha or tracking error (or both) in different ways. We recommend you use the shortest path possible for the sake of time on your exam. For example, if they don’t give you a number for “alpha” or “excess return” then you’ll have to calculate using the CAPM formula.
Step 1: Calculate alpha (excess return): With the data given, you could choose to calculate Jensen’s alpha (using the CAPM formula); but since they give you the portfolio return, the market return, and indicate excess return (portfolio return – market return), we recommend you use what is given (i.e., excess return). Either process should eventually rank the funds in the same order.
Fund A = 12% - 10% = 2%
Fund B = 15% - 10% = 5%
Fund C = 9% - 10% = -1%
Step 2: Calculate tracking error: Again, depending on the data they give you, this can be done different ways. You might be asked to calculate standard deviation manually in this step on your exam, but here they give it to you, so just plug in standard deviation. If, however, they give you a number for tracking error or residual standard deviation, then you would use that number.
Fund A = 15% (given)
Fund B = 18% (given)
Fund C = 11% (given)
Note that the term “residual standard deviation” can also be a substitute for the term “tracking error” in case you see that on your exam.
Step 3: Divide alpha by tracking error.
Fund A = 2%/15% = .1333
Fund B = 5%/18% = .2778
Fund C = -1%/11% = -.0909
Thus, Fund B has the highest information ratio.
Reference: Math for Investment Consultants page 6-16. Key Concepts Slides Section IV.C.
Hillary is 75 years old and has a retirement portfolio of $5 million. The investment policy you and Hillary agreed to allows an allocation of up to 15% in non-liquid alternative investments based on an expected safe withdrawal rate of 5% of total liquid assets in her portfolio. She needs cash each year of roughly $225,000. Hillary’s current allocation to non-liquid alternative investments is $500,000. These are the only non-liquid assets she holds. She would like to raise her investment in venture capital funds to $1 million. What would be most appropriate based on the facts above?
Do not allow any additional funds to be invested in non-liquid alternative investments.
Allow an additional $500,000 investment.
Allow an additional $25,000 investment.
Allow an additional $250,000 investment.
CIMA Section V.F. Portfolio Review and Revisions
The investment policy is designed to predetermine allocations to various asset classes and strategies. This policy allows an allocation of up to $750,000 to non-liquid alternative investments as long as a withdrawal rate of 5% can be used against the liquid portfolio to generate her income need of $225k each year. Her total liquid portfolio is currently $4.5 million ($5 million minus the $500k already invested in non-liquid alternative investments) and 5% of $4.5 million = $225,000 (her cash-flow need). Thus, no additional investment should be made.
A share of stock is purchased at $50 at time t = 0. An additional share is purchased for $60 at time t = 1. The stock pays a dividend of $2 per share at time t = 1 and t = 2. Both shares of stock are sold at $70 at time t = 2.
What is the dollar-weighted rate of return?
What is the time-weighted return?
- Solution: The dollar weighted return = 21.34%
PV (cash outflows) = PV (cash inflows)
$50 $60 $2 $144
+ = + 2
(1 + i) (1 + i) (1 + i)
Notation Used on Most Calculators Numerical Value for This Problem
CF0 -50
CFj -58
CFj 144
%i Compute
You can find i through trial and error, or use a calculator. - Solution: Time-weighted Return
Holding Period 1 = ($60 − $50 + $2) / $50 = 0.24
Holding Period 2 = ($140 − $120 + $4) / $120 = 0.20
Geometric Return = (1.24)(1.20)1/2 – 1 = 0.2198 or 21.98%
R^2=
Beta^2 * (SDEVm^2 / SDEVp^2)
Each of the following is considered important for choosing an appropriate investment benchmark or index for portfolio comparison:
appropriate and accountable, measurable, unambiguous, representative, and investable.
U MARIA? Yeah I’m Maria. I’m the best financial advisor out there. I choose the best benchmarks for my portfolio comparisons. They’re appropriate, accountable, measurable, unambiguous, representative, and investable.
Which of the following is not accurate as they pertain to performance attribution terms?
active asset selection = stock picking
active asset allocation = tactical allocation
active asset selection = technical analysis
active asset allocation = market timing
active asset selection =// technical analysis
CIMA Section V.E. Manager Search, Selection, and Monitoring
Performance Attribution Analysis
The following terms are used interchangeably in IWI materials (e.g., MFIC workbook and CIMA exam formula sheet)
active asset “allocation”
= market timing
= tactical allocation
active asset “selection”
= security selection
= stock picking
