Theory

Question 1

Edwin Elton and Martin Gruber (the main authors of our textbook) often heard investment managers say: „ I followed that rubbish CAPM theory and bought stocks with high betas last year and they did worse than stocks with low betas. This theory is useless:
Explain why the statement of the investment managers is perfectly consistens with the CAPM theory does not invalidate it.

Answer 1

The CAPM is an equilibrium relationship. High ß stocks are expected to give a higher return than low ß stocks because they are more risky. However, this does not mean that they will give a higher return over all intervals of time. In fact, if they always give a higher return, they would be less risky, not more risky than low ß stocks. Rather because they are more risky, they will sometimes produce lower returns. However over long periods of time, the they should on average produce higher returns

Question 2

In their article Kothari, Shanken and Loan (1995) argue that the size and book to market effect in financial data are an artifact if problems inherent in the statistical test finding these effects, such as data mining and database biases.
Describe what they mean by data mining

Answer 2

Data Mining problem occuses if many acadamics use the same dataset to analyse the revaulation between one specific variable (E.g. the expected equity return) and countless other variables. Even if the expected equity return is unrelated to all of them, we would expect that in 95% of all cases there is a spurious relation at standart significance levels. In addition the relationship in the past might not hold in the future. For example. If stock A has high return in the past, it does not mean it will have good performance in the future. However, if stock A give the same level of return in the past and the present, it is just coincidence.

Question 3

Sumarize the compustat biases that they discuss in their artice and that could lead to size and book to market effect.

Answer 3

One Problem with COMPUSTAT is that it only included a firm in the database, if its size crosses a specific threshold. When firm is included in COMPUSTAT, the database then also include the past five years of the which much have necessraly been good years for the firm. In the same vein, distressed firms do no longer need to provide accounting information and are hence not included in COMPUSTAT.

Question 4

You are interest in testing a three facit linear asset pricing model using the method of fama and Macbeth (1973). You test asset are 64 portfolios three way sorted on book-to market, size and momentum. Your sample period ranges from Jauary 1963 to December 2008. What does the term “beta estimaton period” mean in the context of the fama mac beth method? How long is a reasonable beta estimation period?

Answer 4

The length of the beta estimation perdio is the number of ex ante observation used to estimate the beta parameters. It is normally between 4-8 years

Question 5

You are interest in testing a three facit linear asset pricing model using the method of fama and Macbeth (1973). You test asset are 64 portfolios three way sorted on book-to market, size and momentum. Your sample period ranges from Jauary 1963 to December 2008. Explain the first stage (or fist pass) time series regressions, i.e., define the endogenous (Y) variable and the exogenous (X) variables for each time series regression. How many times series regression do you need to ruen? What is the purpose of the time series regressions?= Why is it beneficial to run the time series regression of portfolios?

Answer 5

In the time series regression, you regress the test asset, so there are 64 time series regressions in our case. The purpose of the time series regressions is to obtain beta estimates. The beta estimates usually suffer from lower standart erros thn those of individual equities

Question 6

You are interest in testing a three facit linear asset pricing model using the method of fama and Macbeth (1973). You test asset are 64 portfolios three way sorted on book-to market, size and momentum. Your sample period ranges from Jauary 1963 to December 2008. Explain the second stage (or second pass) cross sectional regression, i.e., define the endorgenous (Y) variable and the exegonueos (X) variable in the one cross sectional regression. How can we intereprt the parameter estimates?

Answer 6

In the cross sectional regression, we regress the realized return of all test asset at the end of the first beta estimation period on the estimated betas.

Question 7

You are interest in testing a three facit linear asset pricing model using the method of fama and Macbeth (1973). You test asset are 64 portfolios three way sorted on book-to market, size and momentum. Your sample period ranges from Jauary 1963 to December 2008. What is meant by rolling forward the beta estimation perdion by one month?

Answer 7

Rolling forward means using a new beta estimation period starting in February 1963 and ending in January 1967 ( if the length of the beta estimation period is four years).

Question 8

You are interest in testing a three facit linear asset pricing model using the method of fama and Macbeth (1973). You test asset are 64 portfolios three way sorted on book-to market, size and momentum. Your sample period ranges from Jauary 1963 to December 2008. How can you obtain the final risk premia (lambda) estimates?

Answer 8

The final risk premia estimate are simply the averages of the cross sectional estimaktes.

Question 9

You would like to test a linear asset pricing model using time series regression. As a result, you regress the realized excees return of one asset onto the pricing factor realization (e.g., in case of the CAPM, you regress the asset excess return onto the market portfolio return. In which case can you reject the asset pricing model? In which case can you not reject the asset pricing model (i.e. what is the statiscal test you use to test the model)?

Answer 9

You test wheter the incerpt is statically different from zero (alpha =0). If it is, you reject the asset pricing model. Otherwise, you cannot reject the model.

Question 10

You would like to test a linear asset pricing model using time series regression. As a result, you regress the realized excees return of one asset onto the pricing factor realization (e.g., in case of the CAPM, you regress the asset excess return onto the market portfolio return. Can you use time series regressions to test all linear asset pricing model? Could you , for example, test the fama and French (1993) model using this methodology? Could you use this methododly to test macroeconomic factor model whose pricing factors are changes in growth expectatios, dedault risk and inflation? In general what is the rule to determine whether a linar asset prcing model can be testes using time series regression?

Answer 10

You can only use time series regression for asset prcing model featuring only traded assets as pricing factor. So you can test the fama and French model with this methodoly, but not a macroeconomic model.

Question 11

You would like to test a linear asset pricing model using time series regression. As a result, you regress the realized excees return of one asset onto the pricing factor realization (e.g., in case of the CAPM, you regress the asset excess return onto the market portfolio return. What are the advantages and disadvantages of the time series methodology?

Answer 11

One advantage is that time series regressions avoid the errors in variables proble,. A disadvantage is that they can pnl ybe employed to one asset at the time. Another disadvantage is that they cannot always be used.

Question 12

Do investors like or dislike increase in the mean return of an asset? Why?

Answer 12

They like increase in the mean, because the mean return can be seen as the expected compensation from an investment (the higher the better)

Question 13

Do investors like or dislike increase in the variance of an asset? Why?

Answer 13

They dislike variance because of risk aversion (and higher probability of potential losses to suffer)

Question 14

Do investors like or dislike increase in the skewness of an asset? Why?

Answer 14

They like positive skewness since positive skewness increases the change of very positive return

Question 15

Do investors like or dislike increase in the kurtisos of an asset? Why?

Answer 15

They dislike kurtisos because the joy they experience from positive return does not coun as much as the pain they expierence from very large negative return.

Question 16

Assume that you use the Elton, Gruber, Brown and Goetzmann (EGB&G 2003) method to find the weights of the optimal mean variance efficient portfolio (this is the method featuring the z-variables-our unknow paratameters, whose optimal values can be derivied from gaussian elimination!) What is the basic intuition behind the EGB&G Methid, i.e., which measure do we maximize to find the optimal portofilio weights= Why do we maximize this measure?

Answer 16

Using this methid, we maximize the sharp ratio, as the mean variance efficient portolio will always feature the highest possible sharp ratio.

Question 17

Assume that you use the Elton, Gruber, Brown and Goetzmann (EGB&G 2003) method to find the weights of the optimal mean variance efficient portfolio (this is the method featuring the z-variables-our unknow paratameters, whose optimal values can be derivied from gaussian elimination!) Does this method (as discussed in the lecture) allow short sales?

Answer 17

The oprimal weights obtained from this method can be negative, which means that short sales are not ruled out

Question 18

Assume that you use the Elton, Gruber, Brown and Goetzmann (EGB&G 2003) method to find the weights of the optimal mean variance efficient portfolio (this is the method featuring the z-variables-our unknow paratameters, whose optimal values can be derivied from gaussian elimination!) Assume we obtain Z(1) = 2 and Z(2) = 1, such that the ratio between the two variables is equal to 2. What implication can we draw from this ratio?

Answer 18

If the Z-ratio is 2, then this means that the second asset should obtain two times the weight of the first asset in the optimal portolio.

Question 19

Assume that you use the Elton, Gruber, Brown and Goetzmann (EGB&G 2003) method to find the weights of the optimal mean variance efficient portfolio (this is the method featuring the z-variables-our unknow paratameters, whose optimal values can be derivied from gaussian elimination!) Why do we derive the optimal portfolio weights by deviding one z-variable by the sum of all z-variables, i.e., what additional constrain does this impost.

Answer 19

Dividing by the sum of the z-vatiables does automatically impost the constrain that the weights of the assets in the optimal portfolio have to sum up the unity

Question 20

What is meant by the statement : “the portfolios must be investable”?

Answer 20

Investable portfolios are portfolios into which equity investors at the time could have put money, i.e., thest are portfolio not using any hinsight information.

Question 21

According to the fama fench model answer the following questions:Carefully define each term in the fama fench formula. What do the beta exposdures stand for? What do the lambdas stand for?

Answer 21

The beta exposures measure comovement btween the asset return and the risk factors. The lambdas give the risk premia, i.e, the extra compensation for bearing one unit of beta risk. The beta coefficient can be obtaim from multiple time series regressions, whereas the lambda coefficnet are often estimated using crs sectional test.

Question 22

According to the fama fench model answer the following questions:How are the SMB and HM zero investment portfolios defines?

Answer 22

HML is a poftfolio long on high book to market socks and short on low book to market stocks, keeping the size dimension constant. SMB is a portfolio long on small and short on large socks, keeping the book-to market deminsion constant.

Question 23

According to the fama fench model answer the following questions: How well does the fama and French model perform in asset pricing tests?

Answer 23

The model performs very well in empirical asset pricing tests (which may not be very surprising)

Question 24

19) Shares of small firms with thinly traded socks tend to show positive CAPM alphas. Is this a violation of the efficient market hypothesis?

Answer 24

Thinly traded stocks will not have a considerable amount of market research performed on the companies they represent. The neglected firm effect implies a greater degree of uncertainty with respect to smaller companies. Moreover, there might be liquidity premium for thinly traded stocks that is not captured by the CAPM. Thus positive CAPM alphas among thinly traded stocks do not necessarily violate the efficient market hypothesis since these higher alphas are actually risk premia, nit market inefficiencies.

Question 25

20) What is an Exchange-traded fund? Give two examples of specific ETFs. What are some advantages they have over ordinary open-end mutual funds? What are some disadvantages?

Answer 25

ETFs allow investors to trade index portfolios. Some examples are spiders (SPY), which track the S&P500 index, diamonds (DIA), which track the Dow Jones Industrial Average, and qubes (QQQQ), which track the NASDAQ 100 index. Other examples are listed in Table 4-3. Advantages - 1. ETFs may be bought and sold during the trading day at prices that reflect the current value of the underlying index. This is different from ordinary open-end mutual funds, which are bought or sold only at the end of the day NAV. 2. ETFs can be sold short. 3. ETFs can be purchased on margin. 4. ETFs may have tax advantages. Managers are not forced to sell securities from a portfolio to meet redemption demands, as they would be with open-end funds. Small investors simply sell their ETF shares to other traders without affecting the composition of the underlying portfolio. Institutional investors who want to sell their shares receive shares of stock in the underlying portfolio. 5. ETFs may be cheaper to buy than mutual funds because they are purchased from brokers. The fund doesn't have to incur the costs of marketing itself, so the investor incurs lower management fees. Disadvantages - 1. ETF prices can differ from NAV by small amounts because of the way they trade. This can lead to arbitrage opportunities for large traders. 2. ETFs must be purchased from brokers for a fee. This makes them more expensive than mutual funds that can be purchased at NAV.

Question 26

21) Briefly discuss the event study method. Music Doctors has a beta of 2.25. The annualized market return yesterday was 12%, and the risk-free rate is currently 4%. You observe that Music Doctors had an annualized return yesterday of 15%. Is there any abnormal return on Music Doctors’ stock? Assuming that markets are efficient, what might justify the non-zero abnormal returns?

Answer 26

An event study is an empirical test which allows the researcher to assess the impact of a particula event on a firm's stock price. To do so, one often uses the index model and estimates et, the residual term which measures the firm-specific component of the stock's return. This variable is the difference between the return the stock would ordinarily earn for a given level of market performance and the actual rate of return on the stock. This measure is often referred to as the abnormal return of the stock. However, it is very difficult to identify the exact point in time that an event becomes public information; thus, the better measure is the cumulative abnormal return, which is the sum of abnormal returns over a period of time (a window around the event date). AR = 15% - (4% + 2.25 (8%)) = -7.0%. A negative abnormal return suggests that there was firm-specific bad news.

Question 27

22) Behavioral finance posits that investors possess behavioral biases. Discuss the importance of behavioral biases then list and explain the four behavioral biases discussed in the text.

Answer 27

•Behavioral biases are important because even if information processing was perfect, individuals may tend to make less-than-fully rational decisions using that information. The four behavioral biases are framing, mental accounting, regret avoidance, and prospect theory (or loss aversion). •Framing refers to the tendency of investors to change preferences due to the way an investment is "framed" (i.e., in terms of risk or in terms of return). •Mental accounting is a specific form of framing where an investor takes a lot of risk with one investment account but little risk with another account. •Regret avoidance refers to the tendency of investors to blame themselves more for an unconventional investment that was unsuccessful than a conventional investment that was unsuccessful. •Prospect theory (loss avoidance) suggests that the investor's utility curve is not concave and defined in terms of wealth. Instead, the investor's utility function would be defined in terms of losses relative to current wealth. Thus, the utility curve is convex to losses and concave to gains giving rise to an s-shaped utility curve.

Question 28

23) Discuss what technical analysis is, what technical analysts do, and the relationship between technical analysis, fundamental analysis, and behavioral finance

Answer 28

* Technical analysis attempts to exploit recurring and predictable patterns in stock prices to generate superior portfolio performance. * To determine recurring patterns, technical analysts examine historical returns by means of charts and or time-series analysis (such as moving averages). * Technical analysts do not deny fundamental analysis but believe that prices adjust slowly to new information. * Therefore, the key is to exploit the slow adjustment to the correct new price when information is released. * Technical analysts also use volume and other data to assess market sentiment in an attempt to ascertain the future direction of the market. * Behaviorists believe that behavioral biases may be related to both price and volume data. Thus, technical analysis can be related to behavioral finance.

Question 29

Consider the regression equation: ri- rf= g0+ g1bi+ g2σ2(ei) + eit where: ri- rt= the average difference between the monthly return on stock i and the monthly risk-free rate bi= the beta of stock i ; σ2(ei) = a measure of the nonsystematic variance of the stock i. If you estimated this regression equation and the CAPM was valid, what kind of estimated coefficients g0, g1i and g2 would you expect? Explain the reasons.

Answer 29

* in this model, the coefficient, g0represents the excess return of the security, which would be zero if the CAPM held. * The variable measured by the coefficient g1 in this model is the market risk premium. * If the CAPM is valid, the excess return on the stock is predicted by the systematic risk of the stock and the excess return on the market, not by the nonsystematic risk of the stock. So the loading of firm specific risk (σ2(ei) ), i.e., g2 should be insignificantly different from zero.

Question 30

25) Although the expectations of increases in future interest rates can result in an upward sloping yield curve; an upward sloping yield curve does not in and of itself imply the expectations of higher future interest rates. Explain using the theories of the term structure of interest rates

Answer 30

The expectations theory states that the forward rate equals the market consensus expectation of future short-term rates. Thus, yield to maturity is determined solely by current and expected future one-period interest rates. An upward sloping, or normal, yield curve would indicate that investors anticipate an increase in interest rates. An inverted, or downward sloping, yield curve would indicate an expectation of decreased interest rates. A horizontal yield curve would indicate an expectation of no interest rate changes. The liquidity preference theory of term structure maintains that investors prefer to be liquid to illiquid, all else equal, and will demand a liquidity premium in order to go long term. Thus, liquidity preference readily explains the upward sloping, or normal, yield curve. However, liquidity preference does not readily explain other yield curve shapes. The effects of possible liquidity premiums confound any simple attempt to extract expectation from the term structure. That is, the upward sloping yield curve may be due to expectations of interest rate increases, or due to the requirement of a liquidity premium, or both. The liquidity premium could more than offset expectations of decreased interest rates, and an upward sloping yield would result

Question 31

26) Discuss duration. Include in your discussion what duration measures, how duration relates to maturity, what variables affect duration, and how duration is used as a portfolio management tool (include some of the problems associated with the use of duration as a portfolio management tool).

Answer 31

Duration is a measure of the time it takes to recoup one's investment in a bond, assuming that one purchased the bond for $1,000. Duration is shorter than term to maturity on coupon bonds as cash flows are received prior to maturity. Duration equals term to maturity for zero-coupon bonds, as no cash flows are received prior to maturity. Duration measures the price sensitivity of a bond with respect to interest rate changes. The longer the maturity of the bond, the lower the coupon rate of the bond, and the lower the yield to maturity of the bond, the greater the duration. Interest-rate risk consists of two components: price risk and reinvestment risk. These two risk components move in opposite direction; if duration equals horizon date, the two types of risk exactly offset each other, resulting in zero net interest-rate risk. This portfolio management strategy is immunization. Some of the problems associated with this strategy are: the portfolio is protected against one interest rate change only; thus, once interest rates change, the portfolio must be rebalanced to maintain immunization; duration assumes a horizontal yield curve (not the shape most commonly observed); duration also assumes that any shifts in the yield curve are parallel (resulting in a continued horizontal yield curve); in addition, the portfolio manager may have trouble locating acceptable bonds that produce immunized portfolios; finally, both duration and horizon dates change with the mere passage of time, but not in a lockstep fashion, thus rebalancing is required. Although immunization is considered a passive bond portfolio management strategy, considerable rebalancing must occur, as indicated above. The portfolio manager must consider the tradeoffs between the transaction costs and not being perfectly immunized at all times

Question 32

Define and discuss the Sharpe | , and the situations in which each measure is the most appropriate measure

Answer 32

* Sharpe's measure, (rP - rf)/σP, is a relative measure of the average portfolio return in excess of the average risk-free return over a period time per unit of risk, as measured by the standard deviation of the returns of the portfolio over that time period. * As the risk measure in the Sharpe measure of portfolio performance evaluation is total risk, this measure is appropriate for portfolio performance evaluation if the portfolio being evaluated represents the investor's complete portfolio of assets.

Question 33

Define and discuss the Traynor | , and the situations in which each measure is the most appropriate measure

Answer 33

• Treynor's measure, (rP - rf)/βP, is a relative measure of the average portfolio return in excess of the average risk-free return over a period of time per unit of risk, as measured by the beta of the portfolio over that time period. • As the risk measure in the Treynor measure of portfolio performance evaluation is beta, or systematic risk, this measure is the appropriate portfolio performance evaluation measure if the portfolio being evaluated is only a small part of a large investment portfolio. This measure is also appropriate for evaluation of managers of "subportfolios" of large funds, such as large pension plans

Question 34

Define and discuss the Jensons | , and the situations in which each measure is the most appropriate measure

Answer 34

• Jensen's measure, P = rP -[rf + P(rM - rf)], is a measure of absolute return (average return on the portfolio over a period of time) over and above that predicted by the CAPM. • As the Jensen measure, or Jensen's alpha, measures the return of a portfolio relative to that predicted by the CAPM, this measure is appropriate for the evaluation of managers of "subportfolios" of large funds. However, the Treynor measure is an even better measure for such a scenario

Question 35

. Why is the M2 measure considered as an improvement over the Sharpe ratio?

Answer 35

• M2 uses the same measure of risk as the Sharpe measure - variation in total return, calculated as the standard deviation. For managed portfolio P an adjusted portfolio P* is formed by combining P with borrowing or lending at the risk-free rate to the point where P* has the same volatility as a market index (M). Then since M and P have the same standard deviation they can be directly compared using the M2 measure. M2 = rP* - rM. If P* outperforms M the measure will be positive, which means the CAL on which P* lies will have a steeper slope than the CML on which M lies. M2 is the distance between the CAL and the CML.

Question 36

What is the problem with using the Sharpe measure for evaluation of an active portfolio management strategy

Answer 36

The Sharpe measure penalizes for portfolio variance. If a portfolio is actively managed, the variance of returns is likely to vary considerably over any time period, thus reflecting poor performance as indicated by the Sharpe measure (unless the portfolio returns are much higher as a result of the active management).

Question 37

29) Explain the three major differences between hedge funds and mutual funds.

Answer 37

Three categories of differences are transparency, investors and investment strategies. • Mutual funds are more highly regulated by the SEC and thus are required to be far more transparent. Hedge funds provide only minimal information about portfolio composition or strategy. • Investors in hedge funds differ in that investment minimums were traditionally set at $250,000 to $1,000,000. While newer hedge funds are starting to reduce the minimum investment to $25,000, this minimum is outside the reach of many mutual fund investors. • Mutual funds must provide an investment strategy and are restricted in the use of leverage, short selling, and in their use of derivatives. Other important differences between these two funds are based on differences in liquidity, and compensation structure.

Question 38

30) Why do the the market model approach and the direct approach yield identical expected returns, but different covariances?

Answer 38

Two methods yield identical expected returns, whle sample covariance are different because signle index model assumes the covariance btween the residual return of securities A, B is 0 . But the direct approach of samplecovariance of the total return incorporates the actual sample covariance of the sample residuals.

Question 39

How would the approach of solving a system of equation (Z1, Z2, Z3. etc.) allow you to find the weights of all portfolios on the efficient frontier, i.e, not only those of the optimal portfolio?

Answer 39

One can find the weight of all portfolios on the efficient frontier, by varying the risk free rate.