FIN 421 MIDTERM
Which of the following statements are true? 1.) As diversification increases, total portfolio variance goes to zero. 2.) No risky asset can lie to the left of the global minimum-variance portfolio. 3.) Indifference curves of one investor cannot intersect.
1 is FALSE: Diversification can only take care of idiosyncratic or unsystematic risk. Systematic risk cannot be diversified. A fully diversified portfolio is thus still exposed to systematic risk. 2 is TRUE: The MVP has the smallest return variance among all combinations of risky assets. Hence, no asset can lie to its left in the mean-variance diagram. 3 is TRUE: No portfolio can be preferred to itself.
Market timing is possible based on which of the following asset allocation rules / portfolios? (circle the ones that are correct)
Answer: A Market timing can be used in conjunction with an allocation rule that uses expected returns as an input. This is only true for the tangency portfolio.
According to the capital asset pricing model, .
Answer: B The SML plots expected returns against betas. All securities should lie on this line. If a security lies above the line, its expected return is higher than implied by the CAPM, therefore the security will be underpriced.
If you believe that the size effect represents an anomaly, you should
Answer: D The size effect states that stocks with a low market capitalization tend to perform well in the subsequent period, and vice versa
You buy 100 shares of ACME for $10 per share. You immediately initiate a stop-loss order at $9 per share and a limit-sell order at $12 per share. What is your maximum possible loss?
Answer: E The maximum loss is all of your investment. Stop-loss just means that your broker will initiate the order at $9 per share, but it does not guarantee that there are buyers. You are selling into a falling price.
If you believe that the momentum effect represents an anomaly, you should
Answer: E The momentum effect states that stocks that did well over the past year tend to perform well in the subsequent period, and vice versa
True or False (Explain): As diversification increases, total portfolio variance goes to zero
Answer: FALSE Diversification can only take care of idiosyncratic or unsystematic risk. Systematic risk cannot be diversified. Full diversification leads essentially to holding the market which still has a sizeable volatility
True or False (Explain): Indifference curves of different investor types cannot intersect.
Answer: FALSE Indifference curves of investors with different risk-return trade-offs will intersect. A risk-averse investor has steeper lines which must intersect the flat lines of risk-tolerant investors.
True or False (Explain): If there are two risky assets and one riskless asset, and the correlation between the risky assets is less than 1, then it is always optimal to hold some positive amount of each risky asset
Answer: FALSE Its easy to think of a graph where the tangency portfolio between the CAL and the efficient frontier lies above both assets. Then, one must be short.
True or False (Explain): Suppose the expected return of Gold is less than the risk free rate, but returns on Gold are actually quite variable. In this case, no risk averse investor should hold Gold in their portfolio.
Answer: FALSE No investor should hold only gold, but (depending on the correlations) a small position in gold might be very valuable for diversification. For small positions, covariances matter, not variances.
True or False (Explain): The CAPM says that the holder of a risky asset should be compensated proportionally to the standard deviation of the asset's return.
Answer: FALSE Only systematic risk (beta) deserves compensation, as nobody is forced to be exposed to idiosyncratic ri
True or False (Explain): If real interest rates are constant, your after-tax real return is independent of the level of inflation.
Answer: FALSE Taxes are based on nominal returns, and inflation is not tax-deductible.
True or False (Explain): Suppose you found that, on average, stocks whose ticker symbols start with "A" underperform stocks that start with "Z". You find that market betas of both sets of stocks are comparable. This violates the basic assumption that returns are simply the fair reward for risk.
Answer: FALSE The return difference could be due to some other (non-market) risk. E.g. Liquidity Risk
True or False (Explain): Suppose there exist two assets A and B in the market, with E(RA) = 0.06 and E(RB) = 0.11. To achieve a portfolio expected return af 0.04, asset B must be sold short.
Answer: TRUE .04 = .06w + (1 − w).11 ⇔ −.05w = −.07 ⇔ w = 1.4 Therefore, 1 − w < −.4 and asset B must be sold short.
True or False (Explain): Suppose you found that, on average, stocks whose ticker symbols start with "A" underperform stocks that start with "Z". You find that market betas of both sets of stocks are comparable. This is evidence against the CAPM.
Answer: TRUE According to the CAPM, stocks with similar betas must have similar returns.
True or False (Explain): No risky asset can lie to the left of the global minimumvariance frontier.
Answer: TRUE By definition the MVF is the envelope around all risky assets, which can at most lie on the frontier but usually to the right. Said differently, it is the smallest variance you 6 can achieve for a given level of return. If we added a risky asset to the left of it, then the MVF would adjust and encompass this asset as well.
True or False (Explain): Suppose that all investors agree that stock A has a mean return of .02 per month and a standard deviation of .05 per month. They further agree that stock B has a mean of .01 and a standard deviation of .07, and that the two stocks have perfectly correlated returns. Then it is not possible that a risk-averse investor would hold a positive amount of each stock.
Answer: TRUE Stock B has a lower mean and a higher risk, but does not provide any diversification benefits because of the perfect correlation. As a result, nobody will buy the stock. It would be optimal to sell stock B short.
True or False (Explain): The "Roll Critique" says that the CAPM is not testable because we cannot observe market returns.
Answer: TRUE The market should include elements like human capital that are unobservable.
True or False (Explain): Indifference curves of one investor cannot intersect.
Answer: TRUE You cannot prefer one portfolio to itself
We often assume that returns follow a normal distribution. Discuss the tradeoffs involved in this assumption.
Answer: The assumption is entirely for convenience and mathematical simplicity. We understand normal distributions well (e.g. the 67% - 95% - 99.7% rule), and even though the density function of the normal distribution does not look simple, the distribution has a few nice properties. For example, the sum of normals is normal (i.e. if stocks are normal, portfolios are as well), and it is straightforward to simulate from a normal distribution. We do not believe that returns are actually normally distributed. Stock Market crashes happen much more frequently than the normal distribution would suggest. As a result, while standard deviation completely describes the risk in a normal distribution, it is not a complete risk measure in reality. It might still be, however, a useful approximation.
Asset A has an expected return of 15% and a Sharpe ratio of .4. Asset B has an expected return of 20% and a Sharpe ratio of .3. A risk-averse investor that can allocate his money between the risk-free asset and only one risky asset would prefer a portfolio using the risk-free asset and .
Asset A Using the risk-free asset, he can invest along any point on the CAL. The slope of the CAL is the sharpe ratio, so asset A gives the better investment opportunities.
When backtesting risk parity portfolios based on on an investment universe that includes both bonds and stocks over 1980 to 2014, one finds that the strategy produces a higher Sharpe ratio than the naive 1/N strategy. Explain why this is the case.
Because interest rates have declined over this sample period, bonds have performed relatively well, i.e. they have had high Sharpe ratios. Because risk parity portfolios allocate large weights to low risk assets, i.e. bonds, they have performed better than strategies that invest more heavily in stocks, such as the 1/N strategy.
Let stock X's standard deviation of return equal 0.50 and stock Y's standard deviation of return equal 0.25. If returns of stock X and stock Y have perfect positive correlation, which portfolio combination represents the minimum variance portfolio?
E) Short 100% Stock X and Buy 200% Stock Y Perfect positive or negative correlation implies that zero standard deviation is attainable. For the perfect positive correlation, draw a straight line through both points and look where it intersects the y−axis. Or do the math: 0 = wX(0.5) + (1 − wX)(.25), and therefore wX = −1
If returns are i.i.d. then A) returns are not predictable B) Cov[rt , rt+1] = 0 C) returns are not autocorrelated D) the expected return is the same in each period E) The risk-return tradeoff is the same for all investment horizons F) all of the above
F) all of the above
True or False (Explain): The CAPM implies that if the variance of a stock is higher than the variance of the market, then the expected return on that stock should be higher than the expected return on the market.
FALSE In a well-diversified portfolio (which the CAPM assumes), what matters is whether or not Cov(Ri , RM) > Var(RM).
True or False (Explain): According to the CAPM, stocks with a beta of zero offer an expected rate of return of zero.
FALSE Stocks with a beta of zero offer an expected rate of return equal to the risk-free rate
True or False (Explain): The CAPM implies that investors require a higher return to hold highly volatile securities.
FALSE The CAPM implies that investors require a higher return to hold securities with the highest systematic risk. Firm-specific risk does not affect the expected return of securities.
True or False (Explain): You can construct a portfolio with a beta of 0.75 by investing 0.75 of the budget in T-Bills and the remainder in the market portfolio
FALSE You need to invest 75% in the market portfolio and 25% in T-bills to get a beta of 0.75
True or False. Risk parity portfolios minimize portfolio variance rather than attempting to diversify in terms of dollars invested.
False. Risk parity portfolios attempt to diversify in terms of risk instead of in terms of dollars invested. The risk parity portfolio differs from the minimum variance portfolio.
Which is NOT a true statement regarding the market portfolio.
It is the tangency point between the capital market line and the indifference curve
You regress excess returns of two different assets A and B onto the market excess return and obtain the following: Does a time-series test provide evidence against the CAPM ?
No, both alphas are statistically insignificant (absolute value of T-stat less 2)
You sort stocks into 10 portfolios based on the last name of the firms' CEO. Portfolio 1 includes all firms with last names A-D, portfolio 2 contains last names E-G etc. You find the following pattern in average excess returns: (a) Do the portfolios with 'extreme last names' have different amounts of risk (according to the CAPM)?
No, the A-D portfolio and the X-Z portfolio have very similar betas (X-coordinates in the figure), and therefore equal amounts of risk in the CAPM sense
You regress excess returns of two different assets A and B onto the market excess return and obtain the following: What does "R-squared" measure?
R-squared is a goodness of fit measure (how much of the variation in returns is explained by the market).
In an Expected return vs. risk diagram, mark two (arbitrary) assets with both different returns and risk levels. Assume you want to form a portfolio of these assets but are not allowed to short any of the assets. Add lines/curves to the diagram that show the return/risk combinations of all possible portfolios when the correlation is
See lecture notes
You sort stocks into 10 portfolios based on the last name of the firms' CEO. Portfolio 1 includes all firms with last names A-D, portfolio 2 contains last names E-G etc. You find the following pattern in average excess returns: What is the alpha of a long-short strategy that exploits this pattern? Illustrate graphically.
The alpha of any portfolio equals its vertical distance from the SML in the plot. Portfolio A-D thus has a large positive alpha whereas portfolio X-Z has a large negative alpha. A strategy exploiting this would buy A-D and sell X-Z, for a total alpha of αA−D −αX−Z. Because αX−Z is negative, the alpha of the strategy is the sum of the absolute values of both alphas.
The beta of a security is
The covariance between the security and the market returns divided by the variance of the market returns
According to the capital asset pricing model,
all securities must lie on the security market line
The relevant measure of the risk of individual securities is
beta
In historical U.S. data, high dividend yields tend to be followed by _________________ excess stock market returns over the subsequent years. Additional evidence for return predictability comes from the present value formula, which implies that returns must be predictable by the dividend yield if dividend growth rates are ___________________ , which in turn is true in the data.
high, not predictable
A security's beta coefficient will be negative if
its returns are negatively correlated with market index returns
The time series approach to testing the CAPM is powerful than the twopass cross-sectional regression approach because it is based on data for
less, a single stock
Efficient portfolios are portfolios that .
offer the highest expected rate of return for the same amount of risk.
The relevant measure of the risk for your overall portfolio is
standard deviation of returns
If returns are i.i.d. then
the expected 2-month log return equals twice the expected 1-month log return the variance of 2-month log returns equals twice the variance of 1-month log returns
The variance of a portfolio of risky securities is .
the weighted sum of the securities' covariances with the portfolio