Everything Flashcards

Question

Why do we want to measure performance?

Answer 1

-identifies talent -Criteria for compensation (only for abnormal returns that cannot be achieved through passive investing) -Incentivizes HF managers to decide well

Answer 2

Alpha divided by idiosyncratic risk Pros: accounts for idiosyncratic risk (deviation from benchmark) Intuitive conceptual interpretation (active return/active risk) Cons: Same as for any measure that uses alpha as input, the same drawbacks as jensen's alpha It needs to be compared, it doesn't say much by itself. IN practice IR of 0.5 is good, IR of >1 is excetional

Answer 3

We choose style analysis to evaluate funds comapred to passive similar styles. So to evaluate fund strategies, in some cases to replicate them, to build liquid alternatives and to manage risk exposure. The process 1. regress fund returns on passive style portfolios/benchmarks 2.Regression coefficients constrainted to be nonnegative (MFs cannot short sell) and sum to 1 -> solver required a. benchmark coefficients reveal implicit weight of each asset class b. intercept measures average return due to security selection and timing c r2 measures % of returrn variation due to style choice rather than selection -> style choice matters more than security selection specifics

Answer 4

-Ambiguity on definitions: what is a value style? -Style drift -Depends on appropriate selection of benchmarks -Not immune to manipulation (return smoothing) -Statistical testing is difficult, bnechmarks are strongly correlateid -Yields average style but does not capture rapid style change

Answer 5

-Can handle any strategy for which passive indices exist -Uses only return information (no holding needed) -Powerful analysis which detects style drift -Gives insights in how to replicate the funds returns

Answer 6

Alpha + RF

Answer 7

-Highly concentrated portfolios -Unstable portfolio weights that change drastically with input changes -Not implementable -> extreme short selling -Not possible to incorporate own view -Variance is not a good risk measure if return distributino is non-normal -Thus often poor out-of sample performance

Answer 8

Constrain the output -No short selling constraint -Restrict maximum weights Improve the inputs -Covariance matrix (by increasing data frequency, factor models and shrinkage methods) -Expected return (by extending data sample and black litterman approach)

Answer 9

-Approach to combine investors own subjective view with markets opinion Steps 1. retrieve equilibrium market weights and compute covariance matrix of assets return using historical data 2. calculate benchmark - implied expected assets return through reverse optimization 3. express investor view Q and confidence level of views omega 4. compute investors adjusted ER

Answer 10

Pros -Avoid extreme portfolios -More stable weights -Allows investors to integrate own views -Ensure that forecasts are internally consistent -Manager does not need to have a view on all assets Cons -Requires assumption about market risk aversion -Unclera how to determine own view and its uncertainty -Assumes that returns follow normal distribution

Answer 11

Correlation of current value with previus value

Answer 12

1. concentration 2. unstable weights 3. unimplementable portfolios 4. can't incorporate own views 5. sometimes returns are nonnormally distributed

Answer 13

Its 1 /24th of a year so 1/42

Answer 14

σ_n^2 = γ * VL + αu_{n-1}^2 + βσ_{n-1}^2 With 7 being gamma, VL being long-term volatility, the second term being alpha * return^2 and the third term being beta * var

Answer 15

σ_n^2 = λσ_{n-1}^2 + (1 - λ)u_{n-1}^2 Lambda * var+ (1-lamda) * return^2

Answer 16

VaR = Pt√TσpN^(-1)(X) With PT = portfolio value N^(-1)(X) equalling Z-value of the Xth percentage

Answer 17

S_t+δt = S_t * e^((rf - (σ^2)/2)δt + σ√δtZ) So stock price * exp (return-var/2)*delta t + stdev * sqrt (delta T) * Z Z being random number of deviations from the mean

Answer 18

Sp = (rp - rf) / σp

Answer 19

αp / σ(εp) So alpha portfolio / idiosyncratic stdev

Answer 20

Tp = (rp - rf) / βp

Answer 21

[ option1* ] = [ r1 g1 ]^-1 [ -Γp ] [ option2* ] [ v0 g2 ] [ -νp ] So Mmult matrix inverse of option greeks * portfolio values Then recalculate delta Hedge delta with -delta stocks

Answer 22

State-prices: qu = (R - D) / (R(U - D)) qd = (U - R) / (R(U - D)) Risk-neutral state prices πU = (R - D) / (U - D) πD = (U - R) / (U - D) With pay-off for risk-neutral needing to be discounted

Answer 23

z = S^(-1)(E(r)^adj - rf) With S being the var/covar matrix and ^-1 being its inverse

Answer 24

1. E(R) market= E(r)_market = Sm* + rf -> so not weights * av. return! 2. Normalization factor: (m^opinion - rf) / (m*^T Sm*) (M^opinon / E(r)) also seems to work! 3. Normalized expected returns E(r)_normalized = Sm*^opinion - rf + rf / (m*^T Sm* + rf) Although old return * normalization factor also seems to work 4. Adjust returns for N individual stock opinions μ^adj_i = μ_i + σ_i,1^2 * τ_1 + ... + σ_i,j^2 * τ_j + ... + σ_i,N^2 * τ_N Which is basically the old stock price + (varstock/varotherstock) * delta for otherstock Of course a delta for the stock itself will have varstock/varstock = 1 and thus be fully incorporated 5. calculate opinion adjusted weights z = S^(-1)(E(r)^adj - rf) With S being var/covar matrix M* being weights M^opinion opinion on market returns

Answer 25

σp^2 = w^T Σw σp^2 is the variance of the portfolio. w is the vector of weights of the assets in the portfolio. w^T is the transpose of the vector of weights. Σ (Sigma) is the covariance matrix of the asset returns.

Answer 26

N(D1) for call options N(-D1) for put option Which is norm.s.dist function (or perhaps normsdist also works)

Answer 27

Average loss within VaR So if 5% VaR would be a loss of 6% which equals 60k The average loss if the loss of 6% is met or exceeded could be 7.5% Then expected shortfall would be 75k

Answer 28

U = e^(stdev*sqrt(delta t) or exp(stdev*sqrt(delta t) D = exp(stdev*-sqrt(delta t)

Answer 29

Create var-covar matrix, and another version where only the variance is included Then weigh them, so for example 0.3 * S + 0.7 * S-shrunk Makes extreme covariances smaller and thus outcomes more realistic

Answer 30

C + Ke^(-rT) = P + S where: C = call premium Ke^(-rT) = present value of the strike P = put premium S = the current price of the underline

Answer 31

First order approximation df = Δ x δS Second order approximation df = Δ x δS + 1/2 Γ x (δS)^2 So you can approximate the delta in option price with delta * delta option price However to be accurate, take this, and 0.5 * gamma * delta stock^2 So for example a delta is 0.6, and gamma is 0.03, stock price increases with 1. Estimated new option price is 0.6 higher (0.6 * 1) Accurate estimate includes gamma: 0.6 * 1 + 0.03 * 0.05 * 1^2 = 0.0615 New delta after price increase is 0.6 + 0.03 = 0.63

Answer 32

Call, puts always have 0 or lower delta.

Answer 33

-Distribution of rates tends to exhibit kurtosis (fat tails) -Lognormal distribution assumed by BS model underestimates the probability of extreme price movements, especially for FX rates -OTM calls and puts have higher probability of ending ITM than under lognormal distribution -> obeserved market prices reflect this probability and are thus higher than implied by BS -So higher prices due to higher implied volatility -Called a smile because the implied volatility for both extremely low and high strike prices is higher, thus creating a smiley without eyes.

Answer 34

-Typically seen for equity options -Stock prices have negative skewness (heavy left tail) -> equity options with lower prices usually have higher volatility -Extreme negative movements are underestimated by BS -OTM call has lower probability of ending up ITM than under lognormal distribution -> lower expected payoff -> lower price and IV -OTM put has higher probability of ending up ITM than underl ognormal distribution -> higher expected payoff -> higher price and IV -Called a skew because volatility decreases as strike price increases

Answer 35

Call prices will be lower, as cash dividends will decrease stock price increases. Vice versa puts will be higher, as price increases are lower. Stock-dividends are more complex, and accounted for in the contract.

Answer 36

They create a levered payout and can thus be useful if you want to achieve something with limited upfront payment. Conversely, risk is higher. Through leverage, we can achieve insurance value. A relatively cheap options can insure against a disaster.

Answer 37

hedging Speculation Arbitrage

Answer 38

-Redundant assets (synthetically) but make risk transfer and speculation cheaper and more effective due to -Reduced TX fees -Lump many transactions together -Provide ways to make leveraged bets -Regulatory arbitrage: sometimes options can circumvent regulatory restrictions

Answer 39

Long stock + short call Reduces volatility by capping upside profits and reducing downside losses. To make money, you should correctly anticipate future stock volatility to be lower than market's expectation.

Answer 40

Long stock, l;ong put Strongest performane during bear markets. Protects the portfolio from decline, but you can capitalize on portfolio returns if the market performs very well.

Answer 41

Long stock, long put, short call (different strikes) Brackets the portfolio betweeen two bounds and reduces the cost of the protective put at the expense of giving up some profit potential.

Answer 42

Bets on volatility. Pay off is a V-shape for a straddle, or a V shape with space in between for a strangle. Straddle is better, but more expensive. Payoff is achieved for both upward and downard volatility.

Answer 43

c + Ke^r-t = p + s0 Use it it to calculate prices, or find out arbitrage opportunities if violated

Answer 44

Price of underlying: positive for call, negative for put Strike price: negative for call, positive for put Time to expiration: unknown Volatility: both positive Interest rate: positive for call, ngative for put Dividends: negative for call, positive for put so meaning: higher strike price is lower value for calls, since the relationship is negative. For interest rates: European Call Options: Increase in Interest Rates: When interest rates increase, the present value of the strike price (which is paid at expiration) decreases, making it less costly to carry the position until expiration. Therefore, it's cheaper to buy the stock at a later date for a fixed price, which increases the value of the call option. Decrease in Interest Rates: Conversely, if interest rates decrease, the present value of the strike price increases, making the option less attractive since it becomes more expensive to buy the stock at the strike price in the future. Hence, the value of the call option decreases. European Put Options: Increase in Interest Rates: An increase in interest rates makes it more attractive to sell the stock at the strike price in the future since the proceeds can be reinvested at the higher rate. Additionally, the cost of holding cash (the proceeds you'd get if you sold the underlying asset now and held the cash until the option expiration) is higher. This makes the put option less valuable. Decrease in Interest Rates: A decrease in interest rates reduces the future value of the cash you would get from selling the underlying asset at the strike price, making the put option more valuable because the alternative (holding cash) is less attractive.

Answer 45

The number of options that need to be held to hedge a stock.. (Payoff up - Payoffdown)/(Return up - Return down) Probably not a formula that needs to be known. The intuition is that you would need 3 options to hedge 5 shares for example. Then the hedge ratio would be 3/5th (or -3/5th?)

Answer 46

Risk-neutral world is a hypothetical world in which investors do not require premium for risk, the expected return on all assets is the risk-free rate, but the option price computed in the risk-neutral world equals the option price in the real world.

Answer 47

1. No TX costs /taxes 2. Riskless borrowing and lending and short selling are possible 3. No arbitrage (These assumptions imply perfect markets) 4. Underlying asset prices follows brownian motion -> lognormal distribution and continuous asset price ( no jumps) 5. No dividends during life of derivative 6. security trading is continuous 7. Rf rate and vol are constant If vol is time varying, asset price no longer has a lognormal distribution so returns are no longer normal. intuition: If we cut δt small enough and add enough time steps, binomial tree converges to distribution behavior of geometric Brownian motion. If stock price follows geometric Brownian motion, option price and stock price depend on the same underlying source of risk. So also, in continuous time we can set up a riskless portfolio consisting of stock and option Hedging argument: choose delta such that the delta of the stock - f is risk-free rate → Continuous rebalancing needed to keep portfolio risk-free Portfolio is riskless (in this small-time interval) and must earn risk-free rate → Derive BS formula by solving PDE Magic → Only volatility matters, we do not need to worry about risk and risk premium if we can hedge away the risk completely (in all states).

Answer 48

No, this information is already built into the formula with the inclusion of the stock price, which already reflects the stock's return and risk characteristics.

Answer 49

N(d1) is the delta for call and N(-d1) is the delta for a put. So appreciation per appreciation of 1 of the underlying. N(d2) is risk-neutral probability that a call will be exercised. K*N(d2) is the expected cost of exercise in the risk neutral world.

Answer 50

Stock delta is always 1, as it always increases by 1 relative to a 1 increase of the underlying (the stock itself) Delta of an option varies. Deep ITM should be close to 1, deep OTM should be close to 0.

Answer 51

1. Investors own estimate Calculate with historical volatility, EWMA, Garch Used as input in BS 2. Implied volatility (forward looking) Solve BS for volatility to determine what volatility is implied Forward looking

Answer 52

Delta: impact of small change in asset price (similar to duration) Gamma:P impact of large change in asset price - 2nd order effect (similar to convexity) Vega: impact of change in volatility Greeks are partial derivatives of the BS formula

Answer 53

Benefits: -Simple to compute in real time (analytical expressions) -Allow us to approximate change in position value when underlying risk factors change -Express exposures of different positions to underlying risk factors in comparable terms (same scale) -They can be aggregated across assets in portfolio -Easy to hedge by trading in derivatives and underlying Drawbacks: -Greeks change when underlying risk factor changes → Should be recomputed frequently and hedge position should be adjusted -Greeks depend on validity of pricing model used to compute them -Greeks for American options need to be computed based on a tree

Answer 54

Delta call = (Cu-Cd)/(Su-Sd) Delta put = (Pu-Pd)/(Su-Sd) Between 0 and 1 for a call and -1 and 0 for a put. Can be higher or lower when positions are aggregated.

Answer 55

The numerical part of a value: So absolute value of -1 equals 1, and absolute value of 1 equals 1. Simply put, you take the value rather than the negative or positive value.

Answer 56

Delta will decrease for an in the money option, and increase for an OTM option. Intuiton is that the longer the maturity, the higher the chance the option may not be ITM/OTM in the end.

Answer 57

Gamma is the amount Delta will increase or decrease if the stock price changes with 1 So for a delta of 0.7 and a gamma of 0.2, if price increases with 1, delta will become 0.68 afterwards So delta is a quick approximation, but you need gamma for the exact figures.

Answer 58

Call options have positive convexity, stock price increase has larger effect on call price than stock price decrease (which is nice for option holder)! This goes for both call & put, it's the same for both Option gamma measures rate of change of delta with respect to price of underlyinhg asset So Delta can be seen as driving speed, gamma can be seen as acceleration

Answer 59

Frequent changes to delta, so frequent need for rebalancing to be delta-neutral, which makes hedging more expensive

Answer 60

is the loss level V during time period of length T that we are X% certain will not be exceeded → with probability X, we will not lose more than V dollars on the portfolio over the next T days.

Answer 61

Portfolio composition (exposure to risk) Investment horizon (size of risk) confidence level (type of risk)

Answer 62

Yes, due to chance.

Answer 63

Pros: -Single number that summarizes total risk of FI → Aggregates all Greek letter for all risk factors underlying portfolio into 1 number -Intuitive: easy to understand for top management Cons: -VaR does not tell how large loss can be if VaR is exceeded -VaR is not an adequate measure of tail risk -VaR is inherently backward-looking → Sensitive to data input → Perform stress test -VaR is not a coherent risk measure for non-normal distributions, VaR of portfolio can exceed sum of VaRs of individual positions because it does not take into account that diversification lowers risk. -The main weakness of VaR is tail risk, because VaR does not take into account the shape of the tail

Answer 64

Pros: -Conceptually simple and historical data usually available -Historical correlation between risk factors automatically -incorporated -VaR can be computed for portfolio with non-linear assets -Non-parametric: no distribution assumptions needed for risk factors Cons: -Depends fully on one historical price path → historical sample may not include any extreme events would produce a too low VaR -Accuracy of VaR depends on number of observations on risk factors → trade-off between timelines (recent observations) and precision (more observations) -Computationally intensive (slow) → portfolio revalued many times

Answer 65

Pros: -Easy to implement and computationally fast (for simple portfolio) Theoretically appealing (based on Markowitz portfolio theory) -Variance-Covariance matrix can be updated using DCC-GARCH models → Can allow for time-varying volatilities and correlations -In theory, VaR estimate more precise than with historical simulations Cons: --If key assumptions fail, VaR estimate can be severely biased (we would prefer less precision over high bias, such as with the historical simulations) -Cannot handle assets that are non-linear in risk factors (options). -Linear models fail to capture skewness in probability distribution of option portfolio, even if stock distribution is normal. When assuming normal distribution, VaR underestimated for negative gamma portfolio and overestimated for positive gamma portfolio. -Cannot handle risk factors that have a non-normal distribution -Estimating variance-covariance matrix of a large portfolio is hard

Answer 66

Pros: -Flexible: can assume various distributions to account for non-normality -Can handle non-linear products, such as options -Does not require a lot of historical data (only for choosing parameters) -Large number of simulations can be generated → Increases precision -VaR can be computed for high confidence levels Cons: -If the assumed return distribution (model risk) is wrong, VaR can be severely biased -Computationally inefficient (slow) because the complete portfolio has to be revalued many times -> may use delta/gamma approximation to speed up the calculation of change in value of some portfolio components

Answer 67

ES is the expected loss during time T conditional on the loss exceeding the Xt percentile of the loss distribution. Meaning it is conditional on exceeding VaR and ES measures expected tail loss, so it takes tail-risk into account.

Answer 68

Pros: -In theory ES is a better risk measure than VaR -Captures risk tail and recognizes diversification benefits -Harder to game by traders than VaR: e.g., selling OTM put options Cons: -More difficult to understand and compute than VaR -ES estimate determined by only a few tail observations → Imprecise -Back-testing of ES calculation more difficult than back-testing VaR -Accuracy of ES directly depends on accuracy of VaR

Answer 69

1. Fat tails, heavier tails and more peaked than expected, very small and very large changes are more likely than the distribution suggests 2. skewness (left skew (positive, large gains are more likely, risk is overestimated) or right skew (negative, lareg losses are more likely, risk is underestimated(

Answer 70

1.5^2*0.15^2+0.04^2 = 0.05225 Stdev = 0.05225^0.5 = 22.85% so don't simply add the two!

Answer 71

I. Volatility is mean reverting, i.e., volatility tends to revert to its long-run mean. If volatility is currently high (low), it tends to gradually decrease (increase) over time. This mean reversion is captured by the first component of the GARCH equation. The higher the gamma coefficient, the stronger the mean reversion in volatility. II. Volatility is time varying. This is captured by the second term of the GARCH equation, which updates the volatility forecast to reflect new information in squared stock returns. The higher the alpha coefficient, the faster the volatility forecast responds to this new information. III. Volatility tends to cluster, i.e., volatility tends to be high (low) for extended periods of time. This persistence in volatility is captured by the last term in the GARCH equation that involves lagged volatility. The higher the beta coefficient, the stronger the persistence in volatility.

Answer 72

Delta T = always in terms of years 0.5 month = 24 periods

Answer 73

Portfolio variance: weight transposed * variance covariance matrix * weight vector.

Answer 74

Multiply gamma with long term variance + alpha * pervios return^2 + beta * Previous variance

Answer 75

=$correlation$*Z1+**SQRT**(1-$correlation$^2)*Z2 The stronger the correlation, the more closly the movements of the second asset will follow the first asset. And this is + second assets will be scaled by the square root of 1 - correlation^2

Answer 76

=AVERAGEIF(M60:M159,"<="&P60)

Answer 77

It approaches 1or -1

Answer 78

-negative of portfolio gamma / the options gamma

Answer 79

1. matrix: Greeks go in rows, and calls in columns 2. portfolio greeks go in table 3. Mmult(mininverse(matrix,vector) Dont forget control shift enter 4. what delta position do we need? (org delta + delta option 1 + delta option 2 5. opposite delta ## Footnote table: Greeks go in rows, and calls in columns

Answer 80

## Footnote Mu is replaced by RF

Answer 81

call Payoff/exp(rf* T ,0)

Answer 82

Delta is change in option value relative to change in stock price * Call option: delta increases with the stock price * If the option is very deep out-of-the-money = line is flat (=close to 0) = unlikely to be exercised at maturity = increase in stock price very little effect on the call as the call price remains very low = Delta is close to zero when the call is very deep out-of-the-money * When the call is deep in-the-money = very likely to be exercised at maturity (right side) = if the underlying stock price increases by 1 dollar, the payoff of the call at maturity will also go up by 1 dollar => resulting, the value of the call almost increases by 1 dollar = delta of the option is close to 1

Answer 83

Long call: long delta Short call: reduced delta, reduced vega total: downside of covered call is the reduced ability to get gains from stock price (delta) Vega: hoping for low vol, so negative vega

Answer 84

investors would like volatility -> a high vega At the money -> delta are slightly higher than 0.5, thats why not 0.5

Answer 85

| = Exp(stock vol*sqrt delta t)

Answer 86

This equation essentially states that the difference between the price of a call option and the price of a put option with the same strike price and expiration date is equal to the difference between the current stock price and the present value of the strike price. Usually when it is asked "what must be the price". you can use a no arbitrage argument.

Answer 87

BXM provides long equity exposure (positive delta) and short volatility exposure (negative vega)

Answer 88

PPUT provides long equity exposure (positive delta) and long volatility exposure (positive vega)

Answer 89

Its often used when you already own the stock. combo of covered call and a protective put. It has a floor and a cap on the price. youre protecting from vol moves, but u cant gain or lose much. You might have a very specific stock. You own stock You hedge against downside; so put When ppl hedge by buying a put option, but with as little upfront capital as possible --> shorting call options. so you cheaply limited downside potential but at the cost of upside potential.

Answer 90

Bull spread occurs when traders use strike prices between the high and low prices at which traders want to trade a security = position gets better when stock price increases. Similar to a collor, but where a collar is a non directional move, a spread is directional. We are betting also on low vol move, but also to go up. Bull with puts advantage; initial cash inflow short 22 dollar strike, in order to make it a bull spread, it needed to be higher than the strike 18 right top purple; short call that we wrote with a lower strike price must be more valuable (faster itm), so the cost of the long puts is more than offset

Answer 91

While bear spread occurs when a trader sells a call option at a strike price, and then buys it at a higher strike price later, = position gets worse when stock price increases. Similar to a collor, but where a collar is a non directional move, a spread is directional. We are betting also on low vol move, but also to go up. bear with calls advantage; initial cash inflow Left top purple; short call that we wrote with a lower strike price must be more valuable (faster itm), so the cost of the long call is more than offset

Answer 92

over next 10 days, you have a 5% to lose at least 1000 euros

Answer 93

- As its measured in euros and you need value of portfolio --> pt - Its a risk measure so sdev; Sdev doesn’t make assets move - you need sth else to make sigma move, Z - its scaled with square root T, as u need horizon, (10 day value at risk, 100 day)

Answer 94

=percentile.inc( all returns, 1- 95% confidence interval/100)

Answer 95

Z3 its not just your normal.s. inverse Z3 is a combo of z1 and z2. z1 force that drives asset 1. and z2 is the internal force of asset2 except asset 2 is not just driven by its own randomness but also of asset 2. The stronger the correlation, the more closly the movements of the second asset will follow the first asset. And this is + second assets will be scaled by the square root of 1 - correlation^2

Answer 96

variance **not** volatility

Answer 97

Multiply gamma with long term variance + alpha * previous return^2 + beta * Previous variance

Answer 98

Delta-normal method yields more precise VaR estimate because the sample SD used to compute the delta-normal VaR is based on all 100 observations in the sample, whereas the sample quantile used to compute VaR in the historical simulation method uses only observations in left tail. In this question, the 99% historical VaR would be the second-largest simulated daily portfolio loss (which is then scaled by the square root of 10 to get 10-day 99% VaR), so it depends on only 2 observations.

Answer 99

At low percentiles, delta-normal simulation might produce lower VaR estimates compared to historic simulation because it assumes a normal distribution and might not adequately capture extreme events or tail risks. This method is less influenced by extreme observations in the historical data and might not fully account for the potential severity of tail events.

Answer 100

=AVERAGEIF(returns,"<="&percentile returns)

Answer 101

EWMA. There should be volatility clustering, so either EWMA or GARCH. GARCH is not suitable due to long-term variance. Because of the capital structure change, the long term variance will be massively under-estimated and this effect will persist for a long time. With EWMA, the historically lower leverage (and therefore also lower variance) washes out at an exponential rate

Answer 102

Intercept(return apple - rf, return s&p 500 - rf) | ALWAYS check time period. Monthly, yearly alpha Y=apple-rf

Answer 103

A private investment pool, open to institutional or wealthy investors, that is largely exempt from SEC regulation and can pursue more speculative investment policies than mutual funds - Idea: Sophisticated/wealthier investors need less protection - Broad term that encompasses funds that follow very different strategies and have different risk and return profile - Hedge fund strategies focused on absolute returns

Answer 104

- more competition - markets more efficient - more regulations (less flexibility) - Financial incentives for managers have become less

Answer 105

Management fee plus incentive/performance fee - management: usually 2% of Asset Under Management + incentive 20% of gains (2/20 scheme) - Incentive fee can be modeled as call option -> may encourage excessive risk taking by HF manager (asymmetric payoff). for every dollar above hurdle, manager get 20 cents

Answer 106

Crowding (people following similar strategy, leads to less returns and could lead to fire sale) style drift lack of liquidity

Answer 107

If fund experiences losses, incentive fee only paid when it makes up for these losses -> creates incentive to shut down fund after poor performance and simply start new fund! "if im underwater, ill just start a new one"

Answer 108

Hedge funds that invest in other hedge funds * Little diversification if underlying HF follow similar strategies * Usually 1% management fee and 10% incentive fee * FoF pays incentive fee to each underlying HF (FoF = fee-on-fee!) * Number of FoFs has dropped after 2008 due to high fees

Answer 109

There is more correlation during recession, which is when you want to be most diversified. The diversification benefits have become less due to the grown size funds. They seem to be correlated to s&p 500 and most strategies correlated to equity but less to the bond market

Answer 110

Directional (bets) * Bets on the direction of financial or economic variables * Examples: increase in S&P 500, decrease in interest rates, etc. * Often based on fundamental investment approach * Typically not market neutral (positive or negative exposure) Non directional (arbitrage: but no free lunches!) * Exploit temporary misalignments in security valuations * Often quantitative investment approach (data mining?) * Buy one security and sell another (e.g., pairs trading, profit from price variations across markets) * Strives to be market neutral * Relative value vs. convergence trades: for latter, convergence period is usually known (e.g., expiration of futures contract)

Answer 111

it is a method of determining an asset’s worth that takes into account the value of similar assets * Pairs trading is a common strategy of relative value funds where a long and short position is initiated for a pair of assets that are highly correlated

Answer 112

It is buying a security with a future delivery date for a low price and selling a similar security, also with a future delivery date, for a higher price * index arbitrage = taking a position in an index futures contract and one in the underlying stock index

Answer 113

Why do we care about alphas and betas? 1. No point to pay fee for beta exposure that you can get yourself through index fund or ETF  only pay for alpha! 2. Allows to check if HF manager follows proclaimed strategy 3. Investor can short market index (futures/ETF) to remove market risk

Answer 114

1. Skill Best managers have incentive to leave MF and start HF due to higher fees + capture large share of own value creation (money wise) 2. Investment flexibility (leverage, short selling, derivates) HF face few restrictions and can follow flexible investment strategies -> use leverage, short selling and derivatives 3. Fraud (insider trading etc) Ponsi scame -> MADOFF 4. Data issues (smoothing, backfilling, survivorship, etc)

Answer 115

- HF returns self-reported and may be **smoothed** over a few months. Possible particularity when fund holds illiquid assets that are not market-to-market often - Santa effect: higher returns reported in December (window dressing) -> 2.5x as large as in other months o Stronger for lower-liquidity funds close to incentive free hurdle - Backfill bias: hedge funds report returns to data providers only if they choose to (not required to report) -> incentive to start reporting when they have been successful - Survivorship bias: unsuccessful funds that cease operation stop reporting -> only successful HF remain in database o Important because of high attrition rate among HF

Answer 116

Sharp ratio based on mean variance theory * SR assumes that risk can be measured by Standard Deviation * Only valid when returns follow normal distribution * Fund may have great SR but extreme downside risk exposure

Answer 117

The strategy is often dynamic and non linear Non-linear HF returns due to market timing * Intercept is alpha, slope is beta  biased! ## Footnote Solution: allow for separate up- and down-market betas

Answer 118

* Manager behaviour is direct response to incentives * HF incentive fees asymmetric and based on short-term performance * Sell deep OTM puts that boost one-year sharp ratio -> downside risk exposure

Answer 119

1. Fund managers invest fraction of their own wealth * “Huge loss of diversification to fund manager” Really? 2. Fund managers want to preserve their reputations * Effective? Wall Street tends to have short memory.. 3. Transparent strategy and reporting of positions * Reduces risk but may also lower performance (copycats) 4. Clawback provision: return fees earned in previous years if subsequent performance is poor -> creates long-term * Easy to implement, used by e.g. Harvard endowment

Answer 120

The given formula's assume that we talk about column vectors. Therefore always make sure you set up your weights and returns are set up in column vectors. Then formula's work as you have studied them. Example: X transposed means that the final result should be a row vector

Answer 121

=mmult(mmult(transpose(w1),varcovar),w2)

Answer 122

1. calc stock statistics 2. calc two random envelope portfolio's using C 3. Standardize the weights 4. calc envelope Portfolio Statistics 5. calc combinations of the envelope portfolios 6. calc portfolio statistics of the combinations

Answer 123

1. calc stock statistics 2. calc envelope portfolio using RF 3. Standardize the weights 4. calc envelope Portfolio Statistics 5. calc combinations of the Market portfolio and rf 6. calc portfolio statistics of the combinations | The MP has the highest sharpe. "Highest return for every unit of risk"

Answer 124

Market weight^2*variance

Answer 125

Intercept(return apple - rf, return s&p 500 - rf) | ALWAYS check time period. Monthly, yearly alpha Y=apple-rf

Answer 126

step 2: standardise ## Footnote Sign next to s is a matrix 1, so multiply var cov with 1 vector

Answer 127

Sharpe is commonly denoted on an annual basis whilst our data is monthly Anualized return - anualized rf / Sqrt(12)* stdev

Answer 128

1. choose some random values for weights 2. make sure to have a total of 100% 3. Calc portfolio statistics including sharpe 4. open solver "max" sharpe by including constraints

Answer 129

1. calculate the weights by use of the market cap 2. make sure to have a total of 100% 3. Calc portfolio statistics

Answer 130

1. expected returns are based on historical returns and those are not good predictors of the future. 2. The variance covariance may contain estimation uncertainty. Its not complete crap but still in some market scenarios. Some expected diversifiers might not be anymore in the future 3. Transaction costs and turnover is high, its difficult to montain. Every month will change the optimal weights, rebalancing. Market cap adjusts automatically. Market cap * price. 4. Takes more effort. The management fee is higher.

Answer 131

output is the factor ## Footnote Our opinions are always in excess of rf / variance of market.

Answer 132

Var cov * marketweights * normalisation + rf Check: mmult weights * new implied returns = your opinion

Answer 133

We use the covariance matrix which makes elegant. (opinion on one stock impacts other stocks) formula: Market implied return + (small component that depends on the covariance of the stock we're adjusting with stock we have opinion about / stock we have opinion about) * opinion always fix opinion and denominator (variances)

Answer 134

## Footnote Look a lot like market portfolio but with adjusted er

Answer 135

1. make a returns row with portfolio returns, replication and error row next to the building block row. Add a weights row above the building blocks 2. Replication formula: sumproduct(buildingblocks, weight row), error formula= portfolio-replication) 3. make an error variance, total weights and r2 cell 4. use solver objective; min error variance with the weights row. Add constraints

Answer 136

The SML is too flat. On average, portfolios with a low beta have historically had positive alpha's and for alpha's its the other way around.

Answer 137

Compensation of manager depends on performance * Hedge funds: incentive fee based on realized fund return * Mutual funds: good performance increases AUM, which increases compensation for fund manager

Answer 138

1. Smoothing returns 2. Non-linear strategies, e.g., writing put options 3. Deviating from proclaimed investment style (style drift) Manipulation is action to increase a fund’s performance measure that does not actually add value for investors

Answer 139

Practice of delaying reporting of true returns to create impression that fund is less risky than it really is (reduce volatility) * In very good months, report smaller profits than actually realized * In very bad months, report smaller losses than actually realized How does smoothing affect performance measures? * Std. dev. of reported returns too low  Sharpe, Sortino, and IR overstated * Correlation of reported returns with factors (and hence betas) biased towards zero  alpha, TR, and IR overstated if factor premiums are +

Answer 140

Autocorrelation in the context of finance refers to the relationship between a financial time series data and its lagged values (values from previous periods). Positive autocorrelation means that the values of a variable (such as fund returns) tend to be positively correlated with their own past values at specific time lags. When discussing fund returns, positive autocorrelation might suggest a practice known as "smoothing." Smoothing refers to the deliberate manipulation of reported returns to present a more stable or consistent performance pattern over time. This can be achieved by fund managers to portray a more favorable picture of the fund's performance, often for marketing or investor retention purposes.

Answer 141

Market timing involves shifting funds between marketindex portfolio and safe asset * Increase exposure to market when market return is higher, lower exposure in bad times -> non-linear relation between portfolio return and market return

Answer 142

Pros * Can handle any strategy for which passive indexes exist * Simple: uses only return information (no holdings needed) * Powerful: can detect if fund deviates from declared style * Gives insights on how to replicate fund’s return -> reverse engineer investment strategies using only historical performance data Cons * Depends on appropriate selection of benchmarks * Not immune to some forms of manipulation (e.g., return smoothing) * Statistical testing difficult if benchmarks are strongly correlated * Yields average style, does not capture rapid style changes

Answer 143

It might increase -> counter intuitive

Answer 144

Sharpe ratio measures return compensation per unit of total risk, with risk measured by std. dev. -> slope of capital allocation line Appropriate when portfolio represents entire investment for an individual -> total volatility matters

Answer 145

1) Noise in estimating style or risk loadings (betas) leads to noisy alpha estimates 2) True factor loadings may be time-varying -> ignoring this leads to biased alphas 3) Factor model can miss important risk/style factor -> also leads to incorrect alpha

Answer 146

Pros: * Simple to compute (linear regression) * Statistical significance easy to test (t-statistic of intercept) * Level has intuitive interpretation (abnormal return) * Direct measure of return added by manager (skill?) Cons: * Noise in beta estimates leads to noise in alpha estimates * Betas may vary over time due to timing or style switching  alpha biased! * Does not distinguish between good and bad betas * Alpha depends on benchmarks (factors) in model * Alpha can be simply boosted by using leverage * Does not account for portfolio size (AUM)

Answer 147

Pros: * Distinguishes between systematic and idiosyncratic risk * Intuitive conceptual interpretation (reward per unit of beta risk) Cons: * Assumes that beta is positive and constant * Does not distinguish between good and bad beta -> most investors only care about downside beta * Requires beta estimation -> sensitive to chosen benchmark * Treynor ratio per se does not say much -> comparison needed

Answer 148

The sharpe ratio

Answer 149

Funds with a negative return distribution

Answer 150

Pros: * Accounts for idiosyncratic risk (deviation from benchmark) * Intuitive conceptual interpretation (active return/active risk) Cons: * Same as for any measure that uses alpha as input * IR per se does not say much  comparison needed * In practice, IR of 0.5 p/a considered “good” and IR > 1.0 “exceptional” * Only 10% of mutual fund managers have IR > 1.0

Answer 151

The information ratio divides the alpha of the portfolio by nonsystematic risk, called “tracking error” in the industry. It measures abnormal return per unit of risk that in principle could be diversified away by holding a market index portfolio If a stock is part of the index market fund, you can use the information ratio to measure the "contribution to the overal sharpe" . a higher information ratio adds more value to the portfolio

Answer 152

When employing a number of managers in a fund, the nonsystematic risk of each will be largely diversified away, so only systematic risk is relevant. The appropriate performance metric when evaluating components of the full risky portfolio is now the Treynor measure. This reward-to-risk ratio divides expected excess return by systematic risk (i.e., by beta).

Answer 153

Sharpe ratio measures return compensation per unit of total risk, with risk measured by std. dev. -> slope of capital allocation line Appropriate when portfolio represents entire investment for an individual -> total volatility matters

Answer 154

Sortino ratio measures return compensation per unit of bad (downside) risk, with risk measured by downside deviation * Downside deviation is std. dev. of all returns < Rf * Idea: upside volatility is beneficial to investors  not a risk * Std. dev. overstates risk for positively skewed return distributions -> Sharpe ratio may increase when removing largest + returns! * Std. dev. understates risk for negatively skewed distributions

Answer 155

Pros: * Explicitly distinguishes between good and bad volatility * Does not assume that returns follow normal distribution * Allows comparison across asset classes (benchmark is Rf) * Intuitive conceptual interpretation (reward per unit of bad risk) Cons: * Noisier than Sharpe ratio when return distribution is symmetric (fewer observations used to compute downside deviation) * Does not distinguish between systematic and idiosyncratic risk * Sortino ratio per se does not say much  comparison needed

Answer 156

Left: positive skewness; trend following hedgefunds right: negative skewness; hedgefund that sell out of the money same sdev, negative skew has way more downside risk right; sdev overstated risk left; understates true risk

Answer 157

Long stock, short call BXM provides long equity exposure (positive delta) and short volatility exposure (negative vega)

Answer 158

long stock, long put Limits downside, unlimited upside but profits will always be lower than the stock PPUT has lowest downside deviation -> Sortino ratios of various strategies very similar PPUT provides long equity exposure (positive delta) and long volatility exposure (positive vega)

Answer 159

lagere sharpe ratio maar hogere sortino ratio, omdat sortino ratio alleen kijkt naar downside risk

Answer 160

long stock, long put, short call different strike prices, brackets portfolio between two bounds and reduces costs of only the protective put at the expense of giving up profit potential

Answer 161

Buying a call with X1 and selling a call with 2x > X1 Buying a put with with X1 and selling a put with X2 > X1 pays off if the underlying appreciates Bull put spread advantage: initial cash inflow

Answer 162

Buying a call with X2 and selling a call with X1 < X2 Buying a put with with X2 and selling a put with X1 < X2 pays off if the underlying depreciates Long in the higher strike price Call bear spread advantage: initial cash inflow

Answer 163

long call and put with same strike price

Answer 164

long call and put with different strike price

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