UOLs

Question 1

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?

Answer 1

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.

Question 2

Discuss empirical evidence regarding the CAPM. Are there certain assets for which the CAPM appears wrong?

Answer 2

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.

Question 3

Roll’s critique. Explain.

Answer 3

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.

Question 4

Jill Crener, the host of TV show Crazy Cash, gives stock recommendations every day and insists following these recommendations will beat the market.

Answer 4

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.

Question 5

Inintech announces that it has discovered a cure for colon cancer. Its share price rises by 45%.

Answer 5

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.

Question 6

If a firm’s stock price falls by more than 2% on any given day, the return is typically positive the following day.

Answer 6

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.

Question 7

The difference between the best performing and worst performing London hedge funds was 86% in 2013.

Answer 7

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.

Question 8

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?

Answer 8

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.

Question 9

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?

Answer 9

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.

Question 10

NPV - IRR different answers when

Answer 10

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.

Question 11

How does the empirical security market line compare to the one predicted by the CAPM?

Answer 11

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.

Question 12

Suppose the CAPM does not hold, is this evidence of the violation of market efficiency?

Answer 12

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.

Question 13

Discuss evidence on ‘anomalies’ such as size, book-to-market, and return predictability.

Answer 13

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.

Question 14

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.

Answer 14

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.

Question 15

Explain the different forms of market efficiency and how they relate to one another.

Answer 15

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.

Question 16

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.

Answer 16

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.

Question 17

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.

Answer 17

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.

Question 18

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.

Answer 18

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.

Question 19

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.

Answer 19

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.

Question 20

Discuss the implication(s) of the number of assets (N) in portfolio management and diversification of risk.

Answer 20

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.

Question 21

Critically assess the validity of the Capital Asset Pricing Model in light of Roll’s critique and other anomalies.

Answer 21

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.

Question 22

Critically assess the empirical evidence for the semi-strong form of market efficiency.

Answer 22

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.

Question 23

Derive the Capital Asset Pricing Model (CAPM)

uol 2011 b

Answer 23

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

Question 24

Critically assess the empirical evidence for the weak form market efficiency.

Answer 24

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.

Question 25

Returns of some stock appear to be weakly but positively correlated in the following week.

Answer 25

Positive correlation among weekly stock return might imply that past returns are not fully incorporated in stock prices. This suggests that the market might not be adhering to the weak form efficiency. However, the correlation is weak, therefore investors might not be able to take economic advantage of it. So the market might still be informationally weak efficient.

Question 26

The top 10 equity investment funds in the UK outperformed the UK market by an average of 5% in 2009.

Answer 26

If investment fund managers are supposed to have superior or private information about the invested companies, then the fact that they can outperform the market might suggest that the strong form efficiency is violated.

However, if these managers do not have superior information, they might just outperform the market by a mere luck. Furthermore, this scenario is only detected in one year. We simply do not have sufficient information to determine whether the market is informationally inefficient.

Question 27

A group of candidates from a famous Business School has created a trading rule which appears to outperform the UK market.

Answer 27

It depends how credible this trading rule is. If the trading rule can indeed outperform the market, then the market is not efficient, as past information does not seem to be fully incorporated in stock prices. However, if this trading rule is factitious, then we have no sufficient information to determine whether the market is inefficient.

Question 28

Royal Petrol plc has just announced that it has discovered a new method to turn domestic wastage into petrol. It share price rises by 5%.

Answer 28

It appears that market responds swiftly to an announcement, suggesting that it is consistent with the semi-strong form efficiency. However, the market is unlikely to be strong form efficient as the privately held information is not fully incorporated in the stock price.

Question 29

In the context of asset pricing in financial markets, define what is meant by market efficiency and explain the different forms it may take.

Answer 29

In an efficient capital market, the current price of an asset is the best estimate of its economic value on the basis of the available evidence (i.e. if an investor has a piece of information relevant to a given asset, it is not possible for the investor to exploit the information to earn a positive net risk-adjusted return if the market for that asset is efficient).

Weak form: Any information which might be contained in past price movements is already reflected in the securities’ prices. Current prices fully reflect all security-market information, including the historical sequence of prices, rates of return, trading volume data, and other
market-generated information. Hence no abnormal return can be made from using this information for, for example, technical analysis.

Semi-strong form: All relevant publicly available information is impounded in security prices. Any new information coming to light which bears on a particular firm will be incorporated into the market price of the security quickly and rationally (in terms of the size and direction of price change). Event studies can be used to assess this response.

Strong-form: All relevant information (including that which is only available to those in privileged positions) is fully reflected in security prices, which is unlikely to hold in practice.

Question 30

An empirical study finds that earnings announcements that are made later than the expected announcement date are more likely to be followed by negative
excess stock returns, when compared to earnings announcements made on time or early. Explain whether this finding provides evidence against semi-strong
form efficiency.

Answer 30

This finding does not provide clear evidence against semi-strong form market efficiency. Earnings announcements may contain either a positive or negative surprise. Delayed earnings announcements may be more likely to convey unanticipated bad news which is followed by a negative market reaction.

Question 31

In the context of testing market efficiency, explain what is meant by the ‘joint hypothesis problem’.

Answer 31

Since the true model that generates expected asset returns is unknown, a proxy must be employed to provide a comparison with actual returns and hence estimate the excess return. So, any test of efficiency is actually a joint test of efficiency and the asset-pricing model. Using a particular pricing model, one might find evidence against market efficiency. However, an alternative explanation is that the market is efficient and the pricing model is wrong.

Question 32

Assess the empirical evidence on market efficiency provided by tests of stock return autocorrelation.

Answer 32

These studies are tests of weak form efficiency which implies that all autocorrelations of stock returns should be zero (i.e. returns are uncorrelated with their own past values). Tests of return autocorrelation show results that vary with the time period and frequency over which returns are calculated. Many studies have found that daily and weekly returns are positively autocorrelated, for example Fama (1965) which is evidence against weak form efficiency. Portfolios of small stocks have been found to have higher positive autocorrelation than those of large stocks (Lo and MacKinlay, 1988), however this could be due to factors
such as infrequent trading rather than informational inefficiency.

Over longer horizons different findings have emerged, for example over 3–5 years negative autocorrelation in stock returns was found by Fama and French (1988) and Poterba and Summers (1988) again suggesting inefficiency. However, this could be due to mean reversion in expected returns over time, not accommodated in the return generating model (the joint hypothesis problem).

Question 33

Discuss asset pricing anomalies that are not consistent with the predictions of the Capital Asset Pricing Model (CAPM). To what extent does the Fama–French (1992) model overcome these problems?

Answer 33

Important anomalies that have been identified include value, size and momentum effects. ‘Value’ stocks with high book value-to-market value ratios have been found to have higher average returns than ‘growth’ stocks with low book-to-market ratios. This is inconsistent with CAPM, which predicts the opposite. Small stocks (those with low market capitalisation) have higher expected returns than predicted by CAPM; large stocks have lower expected returns. Momentum and reversal effects have been observed where compared
with CAPM prediction, stocks that have performed well in the past year have higher expected returns while recent loser stocks have lower expected returns. Stocks that have done poorly in the past several years have higher expected returns than the CAPM prediction, and vice versa for long-run winner stocks.

Fama and French’s model incorporates a factor for the excess return on value stocks, interpreted as capturing risk (because value firms have higher probability of bankruptcy). The higher expected return of small firms is also captured. Empirically, the model has been found to perform better than the CAPM

Question 34

Explain how the Fisher separation theory implies that shareholders can delegate the firms choice of physical investment policy to managers

Answer 34

The Fisher analysis assumes the firm’s set of physical investment opportunities can be ranked according to their return. The firm should optimally invest in all physical investment projects with a return higher than the alternative of financial investment. Ignoring
consumption preference, all firms will make the same optimal physical investment decision from a given set of opportunities. Consumption preferences will then determine the firm’s borrowing or lending policy in the capital market. The implication is that shareholders can
delegate the physical investment decision to a manager (whose preferences may differ from their own) while controlling financial investment policy according to their own preferences.

Question 35

Assess the advantages of the net present value rule for investment appraisal

Answer 35

The firm’s objective is assumed to be the maximisation of shareholder wealth so the firm should select its physical investments using the decision rule that best fits this objective. Hence an investment project should be accepted if its future cash-flows compensate the
investor for the opportunity cost of capital and the initial outlay. The shareholder wealth maximisation objective should also determine the choice of mutually exclusive projects. The NPV rule meets these criteria so is the optimal technique for investment appraisal.

Question 36

Assume that you have collected information on the dates and details of dividend announcements for all FTSE-100 stocks in a particular year. You also have
access to daily price data for all the stocks. Describe the methodology you would use to test semi-strong form efficiency for this stock market.

Answer 36

The primary empirical methodology to test semi-strong form market efficiency is an event study. This provides insights into the speed at which new information is incorporated into stock prices. The first step is to collect the necessary data, taking care to identify precise dates on which the information was released. A measure of the market’s expectations is also
needed to assess the ‘unexpected’ portion of the information in the announcement. Daily price data for a suitable period before and after the event must also be obtained. Suitable time periods for the event and estimation windows must be decided.

Abnormal stock returns for each firm on each date must be calculated by deducting
expected returns from actual returns. Average abnormal returns can then be calculated and
cumulative average abnormal returns plotted against the date. If a clear ‘jump’ in cumulative abnormal returns is observed on the announcement date it provides evidence of market efficiency, as the unexpected information is assimilated into stock prices. Continued drift in abnormal returns after the announcement date suggest slow market reaction to the news which is evidence against informational efficiency, while systematic changes before the
announcement imply information leakage.

Question 37

What are event studies and what are they used for? What type of information efficiency can they test? Explain in detail the hypothesis used in event
studies and how you would design an even time study (hint: consider an event time study around earnings announcements).

Answer 37

Event studies are important for evaluating the semi-strong form of the efficient market hypothesis, as well as studying the effects of key corporate announcements. Explain what the semi-strong form of the efficient market hypothesis means. Next, explain how you would design an event study to examine the price impact of earnings announcements The semi-strong form of the EMH states that all public information is embedded in asset prices. The study should contain an announcement (e.g. earnings announcements) then an announcement
window (including a period leading up to the announcement and a period after the announcement), and investigate the abnormal returns over the announcement window. The test consists of looking at the pattern of abnormal returns. It should have a large jump around the announcement date, and small abnormal returns in the period leading up to the jump and small abnormal returns in the period following the jump. The public announcement should dictate the price jump.