Investments Exam 2

Why do we study the CAPM at all if the same market model can be justified under the APT?

Because the CAPM gives an economic justification of the market as a risk factor. The APT assumes the market portfolio is the single risk factor.

Why do we study the Capital Asset Pricing Model at all if the same market model can be justified under the APT?

Because the CAPM gives an economic justification of the market as a risk factor. The APT assumes the market portfolio is the single risk factor.

In efficient markets, why must the reward-to-risk ratio be the same for all securities? Explain.

Efficient markets should have no arbitrage. If securities have two different reward-to-risk ratios, an arbitrage opportunity exists. Arbitrageurs will sell the security with the low reward-to-risk ratio and buy the security with the high reward-to-risk ratio. This will cause the price on the security to with the high reward- to-risk ratio to go up, which lowers the expected return and thereby decreases the reward-to-risk ratio. Selling the security with the low reward-to-risk ratio causes the price to decrease, thereby raising the expected return, resulting in an increased reward-to-risk ratio. This process will continue until the ratios of the two securities are the same.

What type of securities does your friend appear to invest in? Based on your results, do you agree with your friend's claim of positive alpha? Explain.

To determine the type of securities, look at the betas on the risk factors. In particular, the large beta on the SMB factor and the HML factor suggest investors invest in small stocks with high book-to-market ratios. The friend's claim of 1.17% alpha is relative to the market portfolio. This could be due to either mispricing or un-modeled risk. In your regression against, the Fama-French 3-factor model, which includes 2 additional risk factors, you find an alpha that is extremely small (0.2%) and is statistically insignificant. These results imply that the only reason your friend is getting alpha is due to her high un-modeled risk exposures.

Explain when you would use each of the three fund performance measures: m-square

use this measure if you plan on allocating the entire portfolio to a single fund. The M-Square lets you decide which fund has the best risk-adjusted return.

Explain when you would use each of the three fund performance measures: treynor measure

use this measure if you plan on allocating the portfolio to multiple funds (i.e., you form a fund of funds)

Explain when you would use each of the three fund performance measures: information ratio

use this measure when deciding to add a fund to the benchmark

Define fundamental analysis

when you use all available information to predict returns

Describe how an investor select stocks for a portfolio based on covariances.

1. run regression on risk factors (FF3F) 2. use B to sort stocks and chose stocks w differing B's (covariances)

List and describe the three forms of the Efficient Market Hypothesis discussed in class. which one does the book contradict?

*Weak form* - stock prices reflect all information contained in price history Semi-strong form - stock prices reflect all publicly available information (includes information in price history) Strong form - stock prices reflect all relevant information including inside information (i.e., information privately known by firm only)

List three different assumptions of the CAPM that likely do not hold in reality.

1. All securities are publicly owned, traded and tradeable - not all securities are tradeable (real estate, foreign stocks, etc.) 2. Markets are frictionless - taxes, information costs, transaction costs exist. 3. Investors have a one-period horizon - investors live longer than one period.

List the assumptions of the APT.

1. Asset returns can be described by a factor model 2. There are enough securities in order to be able to construct well-diversified portfolios (i.e. portfolios with no idiosyncratic risk) 3. Financial markets are efficient enough that there are no arbitrage opportunities

List three reasons why the anomalies may not be evidence against market efficiency

1. Data mining - the author may have found a pattern that just works over his time sample 2. True anomalies should be self destructing - the anomalies should have disappeared once the author traded on them (and particularly after the book was published). 3. If the anomalies were so profitable, why is the author not trading on them more (instead of writing a book)?

What is alpha? Describe two interpretations of alpha we discussed in class that highlight the fundamental conflict we discussed throughout the course. Provide a justification for why you would want and not want to buy stocks that have positive alpha.

Alpha may either be interpreted as un-modeled risk or a mispricing by the market. If it is un- modeled risk, then you may be exposing yourself to unknown risk. If it is a mispricing, you may be able to achieve an abnormal return above that which the risk of the stock justifies. The measure of alpha can be interpreted as a manager's skill.

The Arbitrage Pricing Theory shows that we can derive a version of the Capital Asset Pricing Model (CAPM) using much fewer (and more realistic) assumptions. Why do we study the Capital Asset Pricing Model at all if the same market model can be justified under the APT

Although the APT can generate a single market-index model similar to the CAPM, the market factor must be assumed to be the only risk factor. The CAPM is useful because it provides an economic justification for the market factor being the only factor.

The Arbitrage Pricing Theory (APT) implies a version of the CAPM using much fewer (and more realistic) assumptions. What value does the CAPM add relative to the APT?

Because the CAPM gives an economic justification of the market as a risk factor. The APT assumes the market portfolio is the single risk factor.

You have developed a model which includes 5 risk factors. You believe the market uses this model to price assets. Describe how you would test for market efficiency using this asset pricing model.

Check for an Alpha, take stocks, run regression line and check average alpha

Suppose in testing the Capital Asset Pricing Model (CAPM), you find most stocks have alphas that are statistically different from zero. Describe how you would exploit these alphas to profit from this information by achieving abnormal returns.

If many stocks have non-zero alphas, the market portfolio is not the optimal risky portfolio 1. Form an "Active" portfolio by buying those with positive alphas shorting those with negative alphas 2. Apply the Treynor-Black model to calculate the optimal weights of the active portfolio 3. Calculate the optimal risky portfolio weights that combine the active and passive portfolios 4. Choose point on capital allocation line that is best for risk aversion

Describe how you would test for market efficiency using this asset pricing model

If you assume the market should use this model to price assets, then you simply need to run a regression on a lot of stocks and test for non-zero alphas. If alphas are non-zero on average, it may mean the market is inefficient (i.e. mispricing the stocks).

List and describe two examples of evidence that suggest markets are not even weak form efficient?

Momentum (lasts about 1 year) - poor performing stocks continue to poorly perform and well- performing stocks continue to perform well. Markets appear to under-react. Long-term reversal (after 3-5 years) - stocks exhibit (negative serial correlation) at longer horizons. Markets appear to over-react

How would you expect the alpha using the FF3F model to be different from the alpha from the CAPM?

Non-zero alphas under the CAPM suggest missing risk factors. Given the FF3F model includes additional risk factors, the model's alpha should be smaller than the CAPM alpha as the FF3F betas on the 3 risk factors captures more of the abnormal return from the CAPM alpha that is capturing un-modeled risk..

Explain why there is no clear relation between a stock's standard deviation and its expected return.

Should explain that standard deviation includes total risk, which includes unsystematic risk that is diversified away in a portfolio. Since investors do not have to bear this risk, they are not compensated for doing so (there would be an arbitrage opportunity if they were). A perfect answer would also have to point out that total risk and systematic risk are not necessarily related (one stock can have more total risk, but less systematic risk than another stock).

Define technical analysis

Technical analysis is when you use historical stock prices to predict future price changes

In regards to portfolio performance measurements: How is benchmarking related to our use of the CAPM and Fama-French 3 factor model to evaluate portfolio managers?

The CAPM and Fama-French 3-factor model are a way for controlling for risk exposures. The alpha in each model tells us what the expected return of the manager's portfolio is assuming that the risk factors in the models are zero. In essence, the alpha is the risk-adjusted return of the portfolio.

What advantage does the Fama-French 3-Factor model provide relative to the CAPM?

The CAPM has many non-zero alphas (i.e., it fails in the data) , suggesting the CAPM is missing risk factors. The Fama-French 3-factor model provides 2 additional risk factors that better explain stock returns.

If the CAPM were true, what investment advice would it give? Explain.

The CAPM implies the market portfolio is the tangency portfolio. Your optimal investment is to mix the market portfolio with risk-free assets based on your risk preferences.

What is the primary drawback of the FF3F model compared to the CAPM?

The Fama-French model was developed by attempting to explain the failures of the CAPM. It provides no economic reasons for why the SMB and HML factors are risk factors.

Define the version of the Efficient Market Hypothesis the anomalies presented in the seminar seem to contradict

The Semistrong-form version of the EMH says that an investor should not be able to profit from fundamental analysis. Therefore, the anomalies presented in the seminar suggest the market is not semistrong-form efficient.

Define the version(s) of the Efficient Market Hypothesis that profits from technical analysis and fundamental analysis would violate.?

The Weak-form version of the EMH says that an investor should not be able to profit from technical analysis. Therefore, the profits from technical analysis violate weak-form efficiency. The Semistrong-form version of the EMH says that an investor should not be able to profit from fundamental analysis. Therefore, profits from fundamental analysis violate semistrong-form efficiency.

Explain why the alpha is different between the regression specifications.

The alpha under the Fama-French 3 factor model is lower because the CAPM missed substantial risk exposures to small stock risk (SMB) and value stock risk (HML). Including these additional factors captures this risk and the alpha therefore decreases.

How do the different incentives of mutual fund managers and their clients affect the way a manager's performance should be evaluated?

The client's primary incentive is to achieve a good return at low cost. The mutual fund manager wants more money so they focus on high fees and a lot of assets under management. Investors will pay high fees and invest in the fund if it has high returns. Therefore, managers have the incentive to take on more risk to get the higher return. This difference means that the investor must account for the risk that the manager exposes the investor to. Therefore, the investor should use risk-adjusted returns when evaluating a manager's performance. The alpha of a mutual fund is the risk-adjusted return.

Define the joint hypothesis problem and how it applies to the conclusions of your test.

The joint hypothesis problem states that it is impossible to determine whether the model is wrong or the markets are merely mispricing the stock. Therefore, any non-zero alphas found may simply mean the model you developed is wrong. The best we can say is that markets are inefficient relative to your 5-factor model.

Suppose you manage a pension that invests in many well-diversified mutual funds. You would like to add one fund that invests primarily in small stocks. If you have ten funds to choose from, how should you decide which fund to invest in?

The pension is a fund of funds. Therefore, to choose an additional fund to include in the pension portfolio, you should use the Treynor ratio. For each fund, calculate the expected return (average return) of the fund and its beta. Then calculate the Treynor ratio for each fund. Choose the fund with the highest Treynor ratio.

What is the difference between the Conditional CAPM and the Unconditional CAPM? Which version is more likely to be true in the data? Explain

Unconditional CAPM - The original CAPM assumes that the 𝜷𝒊 holds for the life of the security (i.e., use all realized returns) Conditional CAPM - 𝜷𝒊 varies over time (i.e., the beta is only constant for some period of time, for example, 3 years) The conditional CAPM allows for changes in the firm's business over time so it is more likely to be true in the data.

In regards to portfolio performance measurements: Why do we benchmark managers?

We benchmark managers because we want to know their returns after controlling for the risk they take. Even within similar styles, managers may vary widely in the amount of risk they expose their portfolios to.

Is it possible for Stock A to have a greater standard deviation than stock B, but have a lower beta than B? Explain.

Yes. The answer should indicate understanding that standard deviation measures total risk and that beta measures systematic risk. Stock A could have high total risk, but if most of it is diversifiable, then its systematic risk could be low. Students may also mention that sigma and beta are not "on the same scale," which I used to explain how beta could be bigger than sigma and still only be part of what sigma measures.

Should you not invest in a stock if it is a zero NPV investment? Explain.

You should be willing to invest. Financial securities are only positive NPV investments if they are underpriced and you cannot expect to systematically find underpriced securities. A zero NPV investment is one where you are getting a fair (competitively determined) return for the risk you are bearing.

You work for a mutual fund that currently holds the market portfolio. After doing some research, you find a stock with negative alpha. One of your colleagues says the fund should trade on the information. The other colleague says the negative alpha will only hurt your fund's performance. A third colleague reminds you that short selling by mutual funds is not allowed, so you can't trade on the information anyway. Which colleague is correct? Explain.

You should trade on the alpha. Even though it is negative, because the fund owns the market portfolio, it already owns the stock. Therefore, it does not need to necessarily short sell. Instead, it can just sell the holdings of that specific stock in the market portfolio. In essence, it is simply underweighting the stock.

What is the difference in diversifying based on characteristics or covariances?

covariance: SMH & HML use to identify types of stock with respect to how their returns move characteristics: I have part of small stocks and add big stock thinking it'll diversify, but if you don't look at covariance it could still move like a small stock even if its a big stock, not actually diversifying

How would you know if there is an arbitrage opportunity?

determine reward-to-risk ratio, if they differ then there is an arbitrage opportunity