UUNNIIVVEERRSSIIDDAADDEE NNOOVVAA DDEE LLIISSBBOOAA FACULDADE DE ECONOMIA

Second Case:

BETA MANAGEMENT COMPANY

Finance Fall 2006-2007

1) Based on the first three paragraphs of the case, explain Beta Management Company's (BMC) investment strategy. Is it compatible with market efficiency theories?

BMCs Investment Strategy To enhance returns and reduce risks is a general objective of risk-averse investors and shouldnt be considered an investment strategy proper. BMC follows a market timing investment strategy based on two portfolios: the Vanguard Index and money market (i.e., short-term) instruments. When BMC expects the market to rise, it transfers its assets from the money market to the Index (up to a maximum of 99% of total assets), seeking to obtain capital gains; when BMC expects the market to fall, it transfers back the assets from the Index to the money market instruments (down to a minimum of 50%), so as to avoid capital losses. By setting a floor of 50% on the investment on the Index, BMC endeavours to maintain at all times a return spread so as to enhance returns, while seeking to partly capitalize on unpredicted rises (at the cost of losses if the market behaves as predicted). By setting a very high ceiling for the investment in the Index (99%), BMC is willing to take on extra risk to try to fully capitalize on predicted rises. The investment strategy has thus some aggressive elements in it. The objective of risk reduction might better accomplished by setting both a lower ceiling and, particularly, a lower floor. Advantages of the Vanguard Index: - Low transaction costs (important in a market timing strategy, which involves frequent transactions). - Well-diversified portfolio and good proxy for the S&P 500 Index, which is itself a proxy for the market portfolio. Compatibility with Market Efficiency: Under market efficiency asset prices reflect, every moment in time, all the available information. Market efficiency implies one cannot systematically obtain excessive profits if one does not possess a larger information set than the market. A possible exception is the case were efficiency arises exclusively from arbitrage, in which situation a case can be made for a scenario where very good arbitragers may repeatedly beat the market (especially if there are ingenuous players in the market). Market efficiency can be presented in three forms: weak, semi-strong and strong. Weak form efficiency: BMC cannot obtain unusual profits based on the

information contained in past prices, because unexpected variations on a stocks price follow a random walk and cannot therefore be predicted. In this case, it is fairly irrelevant the timing of BMCs stock selling and buying what determines

expected return is the average level of stock held throughout time. Unusual profits would require BMC to have and properly use a larger information set that goes beyond past prices.

Semi-strong form and strong forms: as these forms incorporate the weak form, the

same basic conclusions stated above must apply. The conditions for consistently obtaining unusual returns are even more stringent: in the semi-strong form BMC would need to have access to private information (which does not seem to be the case), and in the strong form such returns would not be possible at all, whatever information set BMC holds.

So, in conclusion, how could BMC have apparently beaten the market in the past?

- BMC might just have been lucky; - BMC may be one of the very good arbitragers; - In case of the weak and semi-strong forms, BMC might have a larger information

set than the market (this does not seem probable); - The market efficiency theory does not apply.

2) Based on the following paragraphs of the case, explain how BMC sought to enhance its investment strategy. Does it seem like a good approach? BMC decided to add individual stocks to its equity portfolio. It preferred to pick smaller companies, reasoning that (i) larger and high-liquidity stocks are thoroughly analysed and so, because of efficient arbitrage, the probability of making excess profits is lower and (ii) smaller companies offer better diversification as BMC was already exposed to big companies through the Vanguard Index. Reason (ii) makes good sense in a risk-averse world. Regarding reason (i), it must be taken into account that even a small number of strong players in the market may be enough to annul high returns. Also, smaller companies may be more risky. BMC focused initially on acquiring shares of one of the two following stocks, reasoning that they were underpriced: California REIT, whose stock price BMC considered to be unduly depressed due

to the World Series earthquake. However, it should be noted that the earthquake affected mainly the state of California which only represents 30% of California REITs portfolio.

Brown Group, Inc.. Regarding this group, BMC remarks that its stock prices are

somewhat sensitive to movements in the stock market, implying a beta that is positive to some significant degree. However, BMC also expects the companys sales to perform well in a recession, which implies, somewhat incongruently, a low beta.

One must also take into account that underpriced stocks may take some time to correct or even plunge further in the meantime. Also, the fact that an individual stock bounces around in price much more than the market is neither unusual nor relevant, as we are not interested in the stocks variance, but in their contribution to the risk of the Vanguard Index portfolio (i.e., its beta). In conclusion, it seems that the strongest reason that has lead BMC to acquire small companies stock is a marketing reason that is, to present a more sophisticated image of investment management to some of its potential clients.

3) Evaluate the risk of the Vanguard Index.

We will take the Vanguard Index as the market portfolio as it is a well-diversified portfolio and good proxy for the S&P 500 Index, which is itself a proxy for the market portfolio. There are two measures of risk that we may be interested in: the standard deviation and the beta. The standard deviation is a measure of risk for a security considered individually, and the beta is the measure of risk for a security in the context of a well-diversified portfolio. As the beta of the market portfolio is, by definition, equal to one, we will only look at the standard deviation of the index. By applying the usual formula,

,1)(Variance deviation Standard

1

2=

==T

t

t

Trr

we get that the unbiased estimation of the standard deviation of the Vanguard Index, obtained from the 24-month return time series, is 4,6063 percentage points (p.p.). 4) Evaluate the risk of the new securities. Which one is riskiest? The appropriate measure of risk for a well diversified portfolio (which is our case) is the beta of the securities. The betas, obtained from the regression of the individual securities on the market portfolio, are:

y = 0,1474x - 0,0243

-0,4000

-0,3000

-0,2000

-0,1000

0,0000

0,1000

0,2000

-0,1000 -0,0500 0,0000 0,0500 0,1000 0,1500

Vanguard Index

Cal

iforn

ia R

EIT

y = 1,1633x - 0,0195

-0,2000

-0,1000

0,0000

0,1000

0,2000

-0,1000 -0,0500 0,0000 0,0500 0,1000 0,1500

Vanguard Index

Bro

wn

Gro

up

Betas California REIT 0,1474 Brown Group, Inc. 1,1633

Conclusion: Brown is riskiest as it has a higher beta. 5) Calculate the standard deviation of a portfolio composed of 99% invested in Vanguard and 1% invested in California REIT. Do the same for a 1% investment in Brown Group. What do you conclude? Explain the result. The standard deviation of the return of a portfolio composed of securities A and B, with respective weights wA and wB, is given by the following formula:

)),(2)()()( 22 BABABBAABBAArwrw rrCovwwrVarwrVarwrwrwVarSD BBAA ++=+=+

where 1

))((),( 1

==

T

rrrrrrCov

T

tBBAA

BA .

SD1%California+99%Vanguard = 4,5680 p.p. < 4,6063 p.p. = SDVanguard SD1%Brown+99%Vanguard = 4,6143 p.p. > 4,6063 p.p. = SDVanguard We conclude that it is possible to diversify away part of the risk of the Vanguard Index by adding the California security to the portfolio. As the beta of the security is lower than one, it was to be expected that, for some weights of the California stock, the risk will be diversified. We have not determined, however, what is the optimal weight for reducing total risk - it could be higher or lower than 1%. We also conclude that if we include the Brown security, the overall risk of the portfolio increases. This is to be expect for all possible positive weights, as the beta of the security is greater than one. 6) Estimate the SML assuming the CAPM holds. Explain the results you have obtained. One could try to estimate the CAPM based on the idea that, in equilibrium, both stocks and the index must belong to the SML. The necessary data would be (expected returns calculated based on the 24-month time series):

Security Expect Return Beta California -2,27% 0,1474

Brown -0,67% 1,1633 Vanguard 1,1% 1

SML

-2,50%

-2,00%

-1,50%

-1,00%

-0,50%

0,00%

0,50%

1,00%

1,50%

0 0,2 0,4 0,6 0,8 1 1,2 1,4

Expe

cted

Ret

urn

Vanguard

Brown

California

The three assets do not lie simultaneously on the same line. Therefore, the CAPM implies that at least one of the assets is not priced correctly. We can try to drop one of the securities and see which SML we obtain. If we drop the Vanguard Index, we get the yellow SML. However, it is incorrect

to drop the Index itself, as this is the asset with the highest probability of being correctly priced.

If we drop the Brown security, we obtain the red SML. However, this SML

cannot be correct as it implies a negative nominal risk-free rate (nominal interest rates cannot be negative).

If we drop the California security, we obtain the green SML. However, this SML

is negatively slopped, and that is not possible because markets recognize a trade-off between systematic risk and return.

So, in conclusion, none of the two securities is correctly priced according to the CAPM. Also, the fact that they show positive betas along with negative returns is inconsistent with the model. A security can have a negative expected return and still be correctly priced according to the CAPM, but that would always imply a negative beta in these cases the security would act as an insurance policy.

A number of reasons can be advanced for explaining this apparent failure of the CAPM, some of which are: - The time series are too short. We would need longer ones to determine the true expected returns (and the other parameters). - The economy is facing a recession and, again, we would need longer time series for the market portfolio. In fact, the American economy was indeed under a recession during the period. - We could be facing a downturn period in the industry cycle of the individual securities. Longer time series would be needed for these. - Past returns do not reflect the agents expectations regarding future returns. - Breakdown of other assumptions of the CAPM, such as homogenous expectations or the existence of a market portfolio. - The CAPM does hold, but securities are overpriced and in the process of correcting. NOTE: if one were trying to estimate the SML using historical data for the risk-free rate or the risk premium, one would have to work in monthly terms, to be consistent with the data for the exercise. 7) Which stock would you recommend adding to the portfolio and why? Can BMC increase returns by adding either stock to its portfolio? Please explain. As we have not been able to properly price the securities, it is difficult to commit to a recommendation. In last the paragraph of the case, it is said that BMCs manager is worried about maintaining risk under control, which may point to adding California REIT as, taking into account the results in 5), California can reduce the overall risk of the portfolio, whereas Brown increases it. However one must also note that California REITs expected return is more negative than Browns. If the true reasons for adding individual securities are the marketing reasons alluded to, then the company might as well add both. Otherwise, it should consider adding none, because of their negative expected values. The CAPM is an equilibrium model (i.e., assets are correctly priced) based on the betas of the securities (which shouldnt change too much, nor too often), and is therefore more in line with a buy and hold investment strategy (i.e., just acquire a well-diversified portfolio and keep it for a certain period). In this case, it is not possible to increase expected returns by adding securities with negative expected returns. It is however possible to increase returns with an efficacious market timing strategy (which allows for returns even in a recession). Finally, as we have seen previously, one must bear in mind that the expected returns we have calculated are likely not the true expected returns.

Daniel Pereira Monteiro Fall 2006/2007