UOLs Flashcards
(37 cards)
Briefly explain the intuition behind the CAPM. According to the CAPM, which characteristic explains whether an asset should have a high or a low return?
The CAPM is an equilibrium model based on certain assumptions about preferences about risk. The intuition is that the average agent holds the market portfolio, therefore any asset with a positive covariance with the market portfolio does poorly when the agent does poorly and is therefore bad insurance. Such assets should have low prices and high returns. Thus,
according to the CAPM, the only characteristic that matters for asset pricing is an asset’s covariance with the market, or equivalently its beta. Assets with high beta should have high expected returns.
Discuss empirical evidence regarding the CAPM. Are there certain assets for which the CAPM appears wrong?
There are multiple anomalies discussed in the subject guide for which the CAPM does not seem to work. Among these are the small stock premium, the value premium, and momentum.
Roll’s critique. Explain.
The CAPM says that the only thing that matters is covariance with the market portfolio. However, according to Rolls critique, we do not actually observe the true market portfolio. We observe the return on a public equity market such as the S&P500, whereas the true market portfolio may contain private equity, corporate debt, real estate, and labour income. Thus, we cannot really determine that the anomalies disprove the CAPM.
Jill Crener, the host of TV show Crazy Cash, gives stock recommendations every day and insists following these recommendations will beat the market.
If Jill’s strategies are indeed profitable than the market is not efficient since everyone has access to them. However, more likely she is just crazy and the recommendations are not profitable.
Inintech announces that it has discovered a cure for colon cancer. Its share price rises by 45%.
It appears that the market responds swiftly to an announcement, suggesting that it is consistent with the semi-strong form efficiency. The market is unlikely to be strong form efficient as the privately held information is not already in the price.
If a firm’s stock price falls by more than 2% on any given day, the return is typically positive the following day.
This is negative autocorrelation which implies that past returns are not fully incorporated in the stock price. This is a violation of weak form efficiency.
The difference between the best performing and worst performing London hedge funds was 86% in 2013.
If managers have superior or private information then this may be a violation of strong form efficiency. However, this may simply be due to luck.
A recent research study found that firms run by CEOs who have family problems (such as a seriously sick child) tend to underperform. You are aware that your cousin, who is married to the CEO of NORNE LLC, is likely to file for divorce. As a result you expect NORNE’s stock price to fall and you short it. Which kind of efficiency must be violated for your expectations to be
correct?
Note that a CEO’s family problems are typically private information, therefore this gives us no evidence that either the weak form or the semi-strong form efficiency are violated. However, if you expect to profit from this trade, you must believe that this market is not strong-form efficient in that private information about the CEO’s personal life is not yet incorporated into prices.
How does the price of a European put option change if the time to maturity rises? If the price of the underlying rises? If the volatility of the underlying rises? If the exercise price rises?
If the volatility rises, the put option price rises. This is because with options, the downside is limited (by zero) and the upside can be very high (unlimited for call options). Increased volatility increases the probability of both.
A rise in time to maturity has exactly the same effect as volatility – there is now more time for the underlying to reach very low or very high prices.
If the price rises, the put option price falls. This is because a put entitles you to sell at a particular fixed price. If the actual price is now higher, the option to sell at a fixed (relatively low) price is less valuable.
If the strike price rises, the put option price rises. This is because a put option entitles the owner to sell the underlying for the exercise (strike) price. Selling at a higher price is good.
If the risk free rate rises the call option value rises. This is because it decreases the present value of the exercise price.
NPV - IRR different answers when
Note that for standard projects IRR and NPV give exactly the same answer since R>IRR implies that the discounted present value is above zero.
However, for non standard projects, they may give different answers. In particular, when we must only choose one project out of many, when the borrowing rate is different from the lending rate, when the discount rate is changing through time, when cash flows are often changing from positive to negative.
If we are able to properly estimate cash flows, growth rates, and discount rates the NPV approach is superior. The NPV approach says to invest whenever a project is increasing firm value – anything else would be wrong! However, in the real world we may not always perfectly estimate cash flows, growth rates, and discount rates. For this reason, IRR may work better in practice even though NPV is theoretically better.
i. IRR does not account for the size or magnitude of the project. It is not a good tool to rank projects.
ii. Cost of capital may vary over time but IRR assumes that any spare cash can be re-invested at the same rate. This might not be realistic.
iii. IRR is not additive and therefore the total IRR of all projects need to be re-computed. NPV has an additive property and therefore the combined effect can be determined easily.
How does the empirical security market line compare to the one predicted by the CAPM?
The empirical line is flatter than the one predicted by theory. Stocks with low betas tend to have higher returns than predicted by CAPM; stocks with high betas tend to have lower returns than predicted by CAPM.
This pattern may be due to mismeasurement of beta. Mismeasurement can be due to Roll’s critique, or for a host of other reasons.
If we are mismeasuring beta, then stocks we are calling high beta are likely to have high beta but not quite as high as we are measuring (beta is the sum of the true beta and an error). In which case, their expected return should be lower than we would be predicting. Similar for low beta stocks, their true beta is not as low as we are measuring. The result would be a flatter line.
Another possible explanation is borrowing constraints. If low risk aversion investors are unable to borrow in order to short low beta stocks and long high beta stocks, they will just be forced to hold long positions in high beta stocks. Thus high beta stocks will be overbought and overvalued and have relatively low returns; low beta stocks will be underbought and undervalued, with relatively high returns.
Suppose the CAPM does not hold, is this evidence of the violation of market efficiency?
It is not necessarily inconsistent with market efficiency. The CAPM is not necessarily the right model to describe all risk. Any firm with higher loading on the ‘true’ risk in the economy should have higher returns.
Multi-factor models attempt to capture the risks in the economy not captured by the CAPM.
Discuss evidence on ‘anomalies’ such as size, book-to-market, and return predictability.
Size: small firms tend to have higher returns than large firms.
Book-to-Market: value firms (firms with high Book/Market ratio) tend to have higher returns than Growth firms (low Book/Market ratio).
At longer horizons stock returns are predictable by variables like P/E, say.
These are not necessarily inconsistent with market efficiency. The CAPM is not necessarily the right model to describe all risk. Any firm with higher loading on the ‘true’ risk in the economy should have higher returns. It
may be that small and value firms are indeed such firms. Multi-factor models attempt to capture the risks in the economy not captured by the CAPM.
Suppose you notice that subsequent stock returns are higher after warm and sunny mornings; stock returns are lower after cold and rainy mornings. Is this market efficient? Which forms of efficiency are violated according to this observation.
This market is is not semi-strong form efficient because morning weather is public information on which anyone can trade. Thus semi-strong-form efficiency is violated, and strong-form efficiency is violated as well. We are given no evidence that weak-form efficiency is violated.
Explain the different forms of market efficiency and how they relate to one another.
A market is efficient if one cannot make economic profits in that market. A market can only be judged efficient or inefficient with respect to certain information set. A market is weak form efficient if prices fully reflect all historical market information like past prices, past data on financial characteristics, etc. A market is semi-strong efficient if prices reflect all public information. A market is strong form efficient if prices reflect all information, both public and private.
Suppose you find that stock returns for all firms whose name starts with A are positively correlated at a five minute frequency. Explain what forms of efficiency this violates.
Positively correlated at five-minute frequency means that if the return over the last five minutes was positive, the return for the next five minutes is likely to be positive too. This suggests a profitable trading strategy, which is a violation of weak form efficiency because past prices and firm names are all publicly available.
Suppose you observe that today’s price-to-dividend ratio forecasts future stock returns, is this necessarily a violation of the Efficient Market Hypothesis? Explain. Briefly review evidence on the forecastability of stock
returns.
Certain variables (such as P/D) forecasting returns is not necessarily a violation of the efficient market hypothesis (EMH). The EMH states that returns should not be predictable once we have accounted for risk. However, if certain assets are more risky, they should have higher returns. Thus if the P/D ratio is also forecasting risk, then it should forecast future returns. Empirical evidence suggests that stock returns are weakly forecastable at longer horizons. Some of the variables that can forecast stock returns are the price-to-dividend ratio, the default spread, the wealth to consumption ratio, past volatility and the corporate spread.
Suppose you find that the stock price of company X falls following those days in which your neighbour has a loud argument with his wife. Explain what forms of efficiency this violates.
This suggests a trading strategy: short company X on any day in which you overhear your neighbours arguing. However, your neighbours arguing is not public information: only you and a few other nearby neighbours are likely to be aware of this event. Therefore this company’s stock is semi-
strong form efficient, but it is not strong form efficient as there is private information that can lead to profits.
Suppose you observe that an estimate of volatility whose value is known today (for example the VIX index) forecasts future stock returns, is this necessarily a violation of the Efficient Market Hypothesis? Explain. Briefly review evidence on the forecastability of stock returns.
Certain variables (such as estimates of volatility) forecasting returns are not necessarily a violation of the Efficient Market Hypothesis (EMH). The EMH states that returns should not be predictable once we have accounted for risk. However, if certain assets are more risky, they should have higher returns. Thus if the VIX index is also forecasting risk, then it should forecast future returns. Empirical evidence suggests that stock returns are weakly forecastable at longer horizons. Some of the variables that can forecast stock returns are the price to dividend ratio, the default spread, the wealth to consumption ratio, and the corporate spread.
Discuss the implication(s) of the number of assets (N) in portfolio management and diversification of risk.
There are a few key implications:
i. As the number of stocks in a portfolio increases, the portfolio’s risk tends towards the average covariance.
ii. As long as the stocks are not perfectly correlated, the portfolio’s risk decreases as we include more stocks.
iii. In terms of portfolio management, one should try to balance out (ii) above to the transaction costs of including additional stocks in a portfolio.
Critically assess the validity of the Capital Asset Pricing Model in light of Roll’s critique and other anomalies.
i. The validity of CAPM depends on whether the market portfolio is mean-variance efficient
ii. The true market portfolio is not observable
iii. Proxies for the market portfolio are often taken from broad-based equity indices which do not contain all the tradable securities or non-financial assets such as real estates, durable goods and even human capital
iv. This renders the CAPM untestable
v. If the CAPM is untestable, then any empirical evidence as argued by Roll would be inconclusive about the validity of the CAPM
vi. Other anomalies such as the size effect, book-to-market ratio and P/E effect seem to suggest that there are risks that are not captured by the CAPM.
Critically assess the empirical evidence for the semi-strong form of market efficiency.
i. The test for semi-strong form efficiency is about how fast and accurate information from an event can be incorporated into prices.
ii. Identify a sample of firms for a particular event.
iii. Measure the ex ante expected return of each firm.
iv. Construct the average abnormal return by comparing the actual average return to the average expected return.
v. The cumulative abnormal returns before and after the event is then examined.
To improve the quality of the answer, you should provide a discussion on the empirical evidence. For example, Asquith and Mullins (1983) suggested that information incorporated within 5–10 minutes and share prices moved up on unexpected dividend announcements. It seems to suggest that such a market is adhering to the semi-strong form efficiency. However, Ball and Brown (1968) argued that unexpected earnings may not be fully incorporated in stock prices. This seems to suggest that empirical evidence for or against market efficiency might be period specific and methodology dependence.
Derive the Capital Asset Pricing Model (CAPM)
uol 2011 b
Еhe marginal rate of substitution(MRS) between the expected return and risk of the market portfolio is defined as the ratio of the partial differentiation of its expected return over the partial differentiation of its expected risk of the portfolio with respect to a. In equilibrium, all marketable assets are included in the market portfolio and there is no excess demand or supply for any individual asset. This implies that
Also note that the MRS at the market portfolio is the same as the slope of the capital market line (CML) at the point of tangency to the efficient frontier. It can be shown that
Critically assess the empirical evidence for the weak form market efficiency.
how the weak form efficiency is tested in empirical studies and in particular, focus on the implications of the findings from the random walk tests, return autocorrelation tests, calendar effects and trading rules.
