Market Efficiency Introduction to Performance Measures

1
Market EfficiencyIntroduction 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.

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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?

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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 SP 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).

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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 SP
  500 the correct benchmark to analyze the
  performance of the fund manager?

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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!

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Barrons Annual Round Table An Example (1/4)

• Heres the question how do some of the top
  superstar analysts 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 Barrons Annual
  Roundtable, Journal of Finance, September 1995.
• Every year, Barrons 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.

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Barrons 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.

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Barrons 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?)

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Barrons Annual Round Table An Example (4/4)

• Over 25 days 4.56 (analysts 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!

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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?

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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.

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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. Jensens alpha Alpha_p Rp - Rf
  Beta_p(Rm-Rf)
• 4. Treynors Square Alpha_p/Beta_p
• Treynors Measure (Rp-Rf)/Beta_p
• 5. Appraisal Ratio (Rp-Rf)/(volatility of
  non-market risk in portfolio)

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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.

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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.

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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.

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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 M2 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 benchmarks volatility is 30.
• We create a portfolio of w0.714 in P and 0.286
  in the riskfree asset. This portfolio now has a
  volatility of (0.714)(42)30.

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M-square 3/3

• The return of this portfolio is now 0.71435
  0.2866 26.7. Comparing with the benchmarks
  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 0.6905-0.73330.30 -1.3.