1. Market Efficiency Introduction to Performance Measures

2. Definition of Market Efficiency Markets are said to be efficient if the stock prices reflect all possible information. Implicitly, we also assume that the price is “correct” - so that the market uses the information to come up with a correct price.

3. Issues of Market Efficiency Are markets efficient? Why is the question important: 1. If markets are efficient, then it would not make sense to spend resources in attempting to beat the market. 2. If markets are efficient, then we should all invest in a passively managed index fund. In this case, portfolio management would be only about portfolio allocation. There has been considerable debate in the last 10 years on whether or not markets are efficient. Perhaps the most convincing evidence for market efficiency is that fact that it is so difficult to beat the market consistently. Perhaps the right question to ask is not whether markets are efficient, but how efficient they are. –How much resources and skills are required for you to get an edge over everybody else in the market?

4. Are Markets Efficient? [1/3] Why is it difficult to answer the question of how efficient markets are? Ask yourself whether the following statements are true or false: 1. To conclude that markets are inefficient, all we need to observe is one person (like Warren Buffet) beating the market. 2. If more than 50% of the mutual fund managers beat the S&P 500 in 2001, then the market must be inefficient. 3. Persistence of performance: if we find a fund manager beating the market 5 years in a row, then he must have the ability to beat the market (and so the market must be inefficient).

5. Are Markets Efficient? [2/3] The answers to all the above questions is “false”. 1. We cannot conclude from observing one manager that the market is inefficient, as that fund manager might just have been lucky. 2. We cannot conclude that markets are efficient or inefficient from observing the average number of managers beating the market. There are two problems here. First, it is possible by sheer chance that more than 50% would beat the market at any given point in time. Second, is the S&P 500 the correct benchmark to analyze the performance of the fund manager?

6. Are Markets Efficient? [3/3] 3. False: Suppose we currently have 5000 mutual fund managers. Then we would expect to find 1/32 of the managers beating the market 5 years in a row - so that 156 managers would beat the market. But what if we observe 200 managers beating the market in 2001? Even then its difficult to conclude anything, because we may not know the exact number of managers in the total population. Usually there is a “survivorship” bias - we only observe those managers that have survived - all those who do badly do not advertise!

7. Barron’s Annual Round Table: An Example (1/4) Here’s the question: how do some of the top superstar analyst’s perform in their stock-picking? Here are some conclusions of a study that considers the recommendation of some top analysts, including Peter Lynch, Neff, Gabelli, etc. “An Analysis of the Recommendation of Superstar Money Managers at the Barron’s Annual Roundtable”, Journal of Finance, September 1995. Every year, Barron’s organizes a round-table discussion, where the 8-12 top analysts are invited in late December, early Jan. Their discussion and recommendations are printed about 2 weeks later.

8. Barron’s Annual Round Table: An Example (2/4) 1. How do you construct a benchmark? In this study, the authors construct a size-based benchmark - using a firm that is closest to the market-cap of the firm that is recommended by the analyst. (Alternatives: control by M/B, P/E, and Beta). The performance measure is the average return over the benchmark over a specified period. 2. Over what period to analyze the returns? In the study, the authors consider a month, 1 year, 2 years, 3 year periods after the publication date of Barrons.

9. Barron’s Annual Round Table: An Example (3/4) 3. To evaluate average performance over all recommendations, should we check whether the magnitude of the average return is greater than the benchmark, or the number of recommended firms that beat the market? 4. How do we control for the market power of the superstar managers? (If Peter Lynch recommends a stock and it goes up, is it because the fundamentals of the company are great, or because Peter Lynch recommended it?)

10. Barron’s Annual Round Table: An Example (4/4) Over 25 days: 4.56% (analyst’s recommendation) vs. 4.23% (for benchmark.). 52% of the 1599 stocks beat their benchmark. Over 1 year: 12.13% vs. 11.93%, and 51% beat the benchmark. Over 2 years: 26.31% vs. 26.69%, and 49.4% beat the benchmark. Over 3 years: 39.99% vs. 40.70%, and 49.3% beat the benchmark. But in the 2-week period between the roundtable meeting and the publication date: 1.36% vs. 0.33, and 60% beat the benchmark!

11. Performance Measurement Given all these problems, we will not focus on the question of whether or not markets are efficient. But we will ask a related, and more practical question: Suppose skilled managers do have skills, then how do we measure it? How do we identify the skilled managers?

12. Performance and Portfolio Strategies Some examples of portfolio strategies/funds: 1. Plain vanilla stock funds: Here, the manager announces his “style” (say, large cap growth) and then attempts to pick the best stocks within that style. Such funds are typically long stock, fully invested, and have limited use of derivatives. 2. Hedge Funds: Can go short, invest in derivatives, etc. 3. Market Timers: Can go long or short, are not fully invested. For each of these strategies, how do we identify the skilled managers? We shall see that it is very, very difficult to answer this question.

13. Some Performance Measures Here are some performance measures that have been used (Refer Chapter 24 of text): 1. Sharpe Ratio: (Rp - Rf)/Sigma_p 2. M-Square (an economic interpretation of the Sharpe ratio) 3. Jensen’s alpha: Alpha_p = Rp - [Rf + Beta_p(Rm-Rf)] 4. Treynor’s Square : Alpha_p/Beta_p Treynor’s Measure: (Rp-Rf)/Beta_p 5. Appraisal Ratio: (Rp-Rf)/(volatility of non-market risk in portfolio)

14. Sharpe Ratio [1/2] We have already seen the Sharpe ratio. It is based on the logic that if you invest in one portfolio, then that portfolio must have the highest possible risk-return tradeoff. It is calculated as follows: 1. Estimate the average return of the portfolio, Rp. 2. Subtract the riskfree rate from the average return to get the excess return: Rp-Rf. 3. Divide the excess return by the standard deviation (or volatility of the portfolio, Sigma_p) to get the Sharpe ratio: (Rp-Rf)/Sigma_p.

15. Sharpe Ratio [1/2] Now we can compare the Sharpe ratio of the portfolio we are evaluating to the Sharpe ratio of the benchmark. Here, a natural benchmark will be the passive index portfolio that proxies for the “market” portfolio. Example: An actively managed portfolio gives you a total return of 35% with a volatility of 42%. In contrast, the market gives you a return of 28% with a volatility of 30%. The riskfree rate is 6%. The Sharpe ratio of the portfolio is 0.69, and that of the market is 0.73. Thus, the portfolio has not performed as well as the benchmark.

16. M Square [1/3] This performance measure is based on the same philosophy as the Sharpe ratio, but is geared towards making it easier to compare the two portfolios. For example, in the previous example, we know that the portfolio P (Sharpe ratio of 0.69) does worse than the benchmark (Sharpe ratio of 0.73), but how much worse? What if the portfolio had a Sharpe ratio of 1.69 and the benchmark had a ratio of 1.73 - is this a better situation or a worse situation? The M Square measure attempts to make such questions easier to answer.

17. The M Square [2/3] The M square measures the difference in the return of the portfolio P and the benchmark M, when portfolio P is mixed with a riskfree asset to make the volatility of portfolio (P + riskfree) the same as the volatility of the benchmark. The M 2 answers the following question: if the investor wants the same volatility as the benchmark, then how much worse or better would the investor do by investing in the actively managed portfolio? Recall that portfolio P has a volatility of 42% and benchmark’s volatility is 30%. We create a portfolio of w=0.714 in P and 0.286 in the riskfree asset. This portfolio now has a volatility of (0.714)(42)=30%.

18. M-square [3/3] The return of this portfolio is now 0.714*35 + 0.286*6 = 26.7%. Comparing with the benchmark’s return of 28%, we see that P has an M Square measure of -1.3%. Thus, for the same volatility, the market gives you an extra return of 1.4%. Alternatively, if you were willing to take the same volatility as the P, then you could have leveraged yourself, invested in the benchmark and earned an extra return. The Sharpe ratio and M Square are related (as can be seen graphically, Figure 24.2 in text): M Square = (Sharpe Ratio of P - Sharpe Ratio of M)(Volatility of M). Thus, for our example, M Square = [0.6905-0.7333]*0.30 = -1.3%.