Finance 460 Final

Short Answer: What does the fact that investors have different types of jobs to do with the success and failure of the CAPM?

A key assumption necessary for the CAPM is that investors are all the same (expect for risk aversion and wealth). When investors are all the same they all want to hold the same tangency portfolio and hence the market is the tangency portfolio giving the CAPM. When investors have jobs that make them sufficiently different then they do not all want to hold the same portfolio and the market no longer must be the tangency portfolio.

Short Answer: What does a large positive beta on SMB tell us?

A large positive beta on SMB tells us that an asset has a large exposure to small stock risk

Short answer: You are considering investing in one of two bonds. Both bonds have a duration of 10. But one bond is more convex. Explain one advantage and one disadvantage of investing in the more convex bond.

An advantage is that the more convex bond will do better with parallel shift in the spot rate (yield) curve. A disadvantage is that the more convex bond will do worse if the spot rate curve steepens.

Short answer: Explain what is meant by we create a custom benchmark by using the Fama French 3 factor model

By a custom benchmark, we mean that the Fama French 3 factor model controls for how much risk each particular manager takes on. The betas will vary with the particular investment strategy of each fund manager

Short answer: How can DFA be a passive fund but still utilize skilled traders to increase investor returns?

DFA believes that the market is efficient but not perfectly - so an extremely uninformed trader might be subject to adverse selection. Basically buying lemons. A skilled trader can help to minimize this risk. Also skilled traders can help to minimize transaction costs while tracking the desired benchmark as closely as possible.

Short answer: Explain briefly DFA's view on the market and one way it uses traders to help achieve superior returns.

DFA views the market as overall efficient and stock picking provides no value. DFA provides clients with access to passively managed funds which expose clients to various systematic risk factors. DFA uses it trades to reduce transaction costs. You could mention one of the following specifics: DFA pursues a block trading strategy by waiting for other to sell it shares at a discount DFA uses it's trades to assure such trades do not expose the firm and its clients to adverse selection DFA refuses to trade with partners who have deceived DFA in the past DFA is slow to exit its positions to avoid moving the price

Short Answer: Explain what risks duration and convexity measure. And give an example of when you would want more risk exposure to each and less exposure to each. (4 examples)

Duration measures our exposure to changes in the level of interest rates. You would like more exposure if you expect interest rate to fall more than the market does and less if you think interest rates will rise more than the market does. Convexity measures our exposure to changes in the slope of interest rates, the yield curve. You would like more exposure if you think the slope will fall more than the market does and less exposure if you think the slope will rise more than the market does. Also acceptable as example for wanting more convexity is if you think the volatility in the level of interest rates will be higher than the market does.

Short answer: How does inflation affect bond returns?

Expected bond returns must be the demanded real interest rate plus expected inflation. Higher expected inflation raises expected bond returns. Realized bond returns are the expected return minus realized inflation. Thus higher than expected inflation lowers real bond returns.

True or False: Bonds with higher yields to maturity have higher expected returns.

False, YTM is simply another way to write a bond's price, it's not the expected return. For example a bond with substantial default risk is likely to have a much higher YTM than its expected return.

True or False: Active mutual funds focus on providing risk exposures (beta) with low turnover and low fees.

False, active funds try to "beat the market", that is provide alpha. To do so they usually require high turnover to purse arbitrage opportunities and typically charge high fees since investors will pay more for alpha than for beta.

True or False: Paying fund managers a percentage of the positive profits (e.g. returns higher than the benchmark) eliminates the incentives to take extra risk because the manager only makes money when you do.

False, because the manager gets more upside return and bears less downside risk he may still wish to take extra risk in hopes of beating his benchmark.

True or False: The CAPM is wrong but the FF3F model is right; there are exactly three sources of systematic risk in equity markets - market risk, size risk (smb), and value vs. growth risk (hml).

False, both the CAPM and FF3F model are models. All models are wrong - but we hope good enough to make useful decisions. There are more sources of systematic risk out there. One such source of risk is momentum.

True or False: If the market is strong form efficient then finding a manager with a large alpha should be difficult.

False, even if the market is strong form efficient and all private information is already included in stock prices you can still find a manager with a large negative alpha. It's very easy to be a bad manager and generate large losses for clients.

True or False: We are willing to pay a manager just as much for expected returns generated from alpha as from betas

False, expected returns generate by betas are due to risk exposures. We are not willing to pay a lot for such expected return because these expected returns are offset by the risk we have to take to earn them. Expected returns generated from alpha on the other is not due to risk (or at least diversifiable risk) so we are wiling to pay a lot for such "free money"

True or False: You have an investment horizon of 1 year. Therefore you would never invest in a 2 year default free bond if it had a lower YTM than the 1 year default free bond.

False, if the interest rates are expected to be significantly lower one year from now than the two year bond may still be an attractive investment despite its low YTM.

True or False: You have no outside income. You have very accurate data on the security market. With this accurate data you calculate the tangency portfolio using MVA. Your investment advisory reminds you that the tangency portfolio is the portfolio with the highest Sharpe ratio. Because of this high Sharpe ratio one such as yourself with no outside income should invest all one's money in the tangency portfolio, forgoing all other financial assets.

False, one should mix the tangency portfolio with the risk free asset to adjust for one's personal risk preferences.

True or False: A more risk averse investor should shift her portfolio from riskier stocks to safer stocks.

False, risk aversion affects how we combine our best mix of risky assets with the risk free asset. Risk aversion does not affect how we mix risky securities.

True or False: To run MVA you simply need to calculate the mean and variance covariance data from past data

False, simply using past data is problematic for many reasons. One issue is that future may be different from the past. Even if the future looks like the past, sampling error may distort our estimates of what the future will look like

True or False: Because the FF3F model corrects for the risks missed by the CAPM, the alpha of a portfolio manager under the FF3F model is a true measure of her skill.

False, the alpha under the FF3F models a better measure of skill than the CAPM because it captures these additional risks. However the FF3F model does not capture all risks. Models are never true; they are always approximations of reality.

True or False: Someone who has a large fraction of her wealth in an untradeable private business which is volatile and is strongly positively correlated with the market should invest heavily in the stock market to help diversify this risk and little in bonds.

False, the high correlation with the market makes investing in the market a poor diversification tool. Hence such an investor should invest a lot in bonds a little in the market.

True or False: Small stocks have had higher average returns than big stocks for decades. This means we should add more small stocks to our portfolio.

False, the higher returns on small stocks is due to the extra risk of small stocks. We should only add small stocks to our portfolio if we want this extra risk exposure.

True or False: You work for Zynga which makes a large portion of its income from individuals who access their games through Facebook. Purchasing a large number of shares of Facebook and adding them to your portfolio is a good idea.

False, the income from your job is highly correlated with Facebook; so adding shares of Facebook to your portfolio amplifies this exposure. You would rather not hold Facebook stock or short shares of Facebook if possible.

True or False: Because of the potential for diversification if two stocks are not perfectly correlated then a portfolio formed by equally weighting each security must be the safest investment when compared to the other options of investing in either security alone.

False, there does exist a mix between the two securities that is safer, but an even mix in not necessarily safe. If one security is very volatile and the other not you would do better investing in only the low volatility security than in the evenly mixed strategy.

True or False: We know by mixing securities we can diversify and lower our portfolio's standard deviation. Thus whenever we evenly mix two securities that are not perfectly correlated, the SR of this mixed portfolio will be higher than the SR of both the individual securities when considered separately.

False, there exists a mix of these securities that will increase the SR, but this mix need not be 50:50. A 50:50 mix can lower the SR compared to the individual security with the best SR. Consider the example of two uncorrelated stocks, one of which returns 1% excess return and 100% standard and one stock that returns 100% excess return and 1% standard deviation. Mixing these evenly lowers the SR compared to the SR of the second stock.

True or False: We only want to pay our managers for alpha, never for beta.

False, usually we want to pay managers for alpha. And we do not want to pay a manager for providing us access to easily available beta such as general market exposure. We may however be willing to pay a manager a modest amount for beta exposure if the exposure is difficult for us to replicate. Think about DFAs profits from selling size and value exposure.

True or False: If markets are semi-strong form efficient, then subscribing to the WSJ will allow you to find many arbitrage opportunities.

False, when the market is semi-strong form efficient all public information is quickly and accurately reflected in prices. This means the information in the WSJ is already in prices; so it will not be helpful in finding arbitrage opportunities.

True or false: All we need to know about a hedge fund is its Sharpe ratio.

False, while the Sharpe ratio is a useful piece of information to have about a fund it provides us with an incomplete picture of the fund. If we are going to invest all our wealth in a hedge fund the Sharpe ratio would be sufficient. However If we are only going to invest a fraction of our wealth then we need more information than the Sharpe ratio to understand how the hedge fund will mix with the rest of our portfolio.

True or False: You see an unusually upward sloping yield curve. This means you should invest in short term bonds and avoid long term bonds.

False, while the upwardly sloping yield curve may indicate that the market expects interest rates to rise, there is no need to avoid long term bonds. The long term bonds already have the market's expectation for higher interest rates included in their current prices.

Short answer: How does evaluating many managers with the Fama French 3 factor model create problems for us?

For a single manager we can evaluate performance with the manager's alpha and the t-stat of that alpha. If the t-stat is higher than 2 we are 95% confident that the manager's alpha is not simply due to chance. However if we have many managers, we are guaranteed to find some with high t-stats. Hence this complicates our analysis.

Short Answer: Explain what illiquidity and leverage have to do with hedge funds.

Hedge funds often invest in illiquid assets. Illiquid assets often lack accurate price information between trades. This inaccurate information causes a fund's market beta to appear lower than it really is and hence increases the funds alpha. Also acceptable for partial credit is that this illiquidity makes hedge funds risky. Hedge funds often have high leverage. This leverage may be valuable to investors as they cannot access such high leverage otherwise. Also acceptable: this leverage makes hedge funds risky because even small losses in the underlying asset value translate into large losses for the hedge fund investors.

Short answer: if the tangency portfolio has a weight of 50% in SMB what does this tell us we should do with our small and big stock investments?

If the tangency portfolio has a weight of 50% in SMB this means we want to put 50% of our portfolio value long in small stocks and 50% of our portfolio value short in big stocks.

Short answer: You manage a default free treasury bond fund and must maintain a portfolio with a constant duration of 10 years. You may also only take long positions in government bonds. You think the yield curve will soon steepen. What should you do?

If you think the yield curve will steepen you should lower the convexity of your bond portfolio to minimize this risk.

Short Answer: Explain the effect of hedge funds holding illiquid assets on our ability to measure a hedge fund manager's skill? How do we deal with this effect?

Illiquid assets often lack accurate price information between trades. This inaccurate information causes a fund's market beta to appear lower than it really is and for this illiquidity by including lags of the market return in our regression.

Short answer: What is the danger of including assets that are too similar (Ford and GM stocks) as separate assets in mean variance analysis?

Including assets that are too similar can make it appear that there is a near arbitrage opportunity when in reality no such opportunity exists. The mean variance math will give you a portfolio that goes very long the asset of the pair that happened to do slightly better by just chance and go really short the asset that did worse just by chance. A useless and non-implementable advice

Short answer: Tell me three distinct interpretations of alpha

Intercept of a regression Model error or how wrong our model is Measurement noise or short-term error in our model An investment opportunity at the stock, security or portfolio level A measure of manager skill

Short answer: How is using MVA on factors related to the products sold by DFA?

MVA on the factors tells us how to construct our optimal portfolio out of the fundamental factor risks in the economy. DFA sells the portfolios, like small stocks portfolios that we need to implement the advice of MVA

Short answer: Provide one potential solution for implementing MVA effectively and explain why it helps

One possible solution is to group assets into classes based on their similarity. This helps because (1) we have fewer parameters to estimate, (2) the classes average many assets making our parameter estimates more accurate and (3) by limiting the appearance of pseudo-arbitrage opportunities that can appear if we include similar assets as separate investment choices

Short answer: Why do we need to be careful when investing simultaneously in many different hedge funds?

Part of the value of hedge funds is that they take undiversified bets. If their bets turn out well, due to superior information or skill of the manager, we profit handsomely. The danger of investing in many different hedge funds is the managers may take offsetting bets. Thus we could end up with a position close to the overall market, yet still be paying very high fees.

Short answer: Suppose the CAPM holds exactly. What is the optimal way to invest in equity markets and why?

The CAPM tells us that the market it the tangency portfolio. Hence you want to invest passively in the market.

Short answer: Explain when and why you can and cannot use the Sharpe ratio as a good measure of the risk return trade off.

The SR can be used when considering an investment of your total wealth. In that case the variance in the denominator is a good measure of risk. When considering only partial investments of your wealth the SR cannot be used. In those cases the variance in the denominator does not properly measure how assets will combine in your portfolio.

Short answer: Suppose Germany decides to guarantee all Greek bonds. What should we expect to happen to the yields on German and Greek bonds?

The guarantee by Germany makes the Greek bonds very similar to the German bonds. Hence we should see the yields on the two bonds converge.

Short answer: If the CAPM were true what investment advice would it give?

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

Short answer: Explain why there is not an arbitrage opportunity available in investing in small stocks or value stock despite their large alphas under the CAPM

Though small stocks and value stocks have large alphas under the CAPM we cannot take advantage of these alpha because we must still retain substantial residual risk if we tilt our portfolio toward these assets. We would have such risk because small stocks move together and value stocks move together. (Seen in plots of these stocks CAPM residuals)

Short answer: Why might an investor without a job or an other source of income be willing to tilt his portfolio (away from the market portfolio) toward value stocks but not toward oil stocks?

Tilting the portfolio away from the market portfolio increases the risk of the portfolio. In the case of the tilt toward value stocks this increased risk is a form of systematic risk that comes with risk premium. In the case of oil stocks much of the additional risk is idiosyncratic and does not come with a risk premium.

True or False: If the CAPM is true then investing in the market mixed with the risk free asset is the best investment you can make.

True, if the CAPM is true then the market is the tangency portfolio. This means that the market mixed with the risk free asset gives the highest Sharpe ratio - the tangency portfolio is the best investment.

True or False: You are worried that the Federal Reserve is printing lots of money to stimulate the economy. Shifting your portfolio of bonds toward shorter term bonds and away from longer tern nominal bonds is a good idea.

True, printing too much money will create inflation. Long term bonds are more exposed to inflation risk than short term bonds. Shifting toward short term bonds lessens your inflation risk exposure.

True or false: Investing across more risk factors improves our Sharpe Ratio

True, provided the factors are not perfectly correlated we can gain diversification benefit by investing in multiple factors. Diversification lowers the risk of our portfolio hence increases its Sharpe ratio.

True or False: The Fama French 3 factor model fits the data better than the CAPM

True, the CAPM does a particularly poor job explaining the returns of small stocks, value stocks, and growth stocks. The Fama French 3 factor model adds two new factors SMB and HML which better explain the returns of these stocks

True or False: We only need historical return information to evaluate a manager's past performance

True, to evaluate a manager we simply need her historical returns to run the Fama French 3 factor model. The model then provides us a measure of the manager's risk exposures and skill (alpha).

True or False: If the CAPM is true then investing in a passive mutual fund that mimicks the market return (ex: Vanguard total index) is the optimal investment strategy for the risky portion of your portfolio.

True, under the CAPM the market is the tangency portfolio. Our optimal investment strategy is to mix the market portfolio with the risk free asset.

Short Answer: Why do we benchmark managers? And how is benchmarking related to our use of the CAPM and FF3M to evaluate portfolio managers?

We benchmark managers because we must control for the amount of risk that they expose us to when evaluating their returns. Using the CAPM or FF3M allows us to more precisely benchmark our managers. These methods rely on how their returns actually behave to form the benchmark rather than simply choosing a pre-specified benchmark.

Short answer: Alpha - How do we measure it? What is it? How do we use it (give two distinct interpretations of it)? And explain how these two interpretations highlight a fundamental conflict in using alpha that we discussed throughout the course.

We measure alpha as the intercept of a regression. Alpha is the excess return beyond that required for risk. We use alpha to evaluate our model - it's our model's error. And we use alpha to evaluate investment opportunities or managers. The fundamental conflict is that alpha indicates something is wrong: either with our model or how other investors are pricing assets. If other investors are wrong, we've found an investment opportunity. But if our model is wrong we have not found an investment opportunity.

Short answer: How do we measure a security's alpha?

We measure alpha relative to a model using a regression of the security's return on a series of risk factors such as the market, smb, or hml. Alpha is the intercept of this regression.

Short answer: Explain how hedge funds investing in illiquid assets can create problems for our evaluation of their skill.

When hedge funds invest in illiquid assets the prices they report may be inaccurate, with gains and losses being reflected only slowly in the funds' reported returns. These stale prices will make funds' appear to be less affected by market movements than they truly are. Thus when using our standard factor models (the CAPM or FF3F) the funds will appear safer than they really are, artificially inflating the funds' alphas.

Short answer: Interest rates are at historically low levels. How does this make default free bond funds particularly risky right now?

When interest rates are low, bond durations are high. This means bond prices will fall sharply for even small increases in interest rates.