Chapter 13 – Performance Evaluation and Risk Management
13.1 Active and Passive Portfolio Management
Passive Portfolio Management
- Investors can either follow an active strategy or a passive strategy after they form their portfolio
- Investors who choose passive management do not change the composition of their portfolio. A Buy and Hold strategy
involves buying financial instruments, forming the portfolio, and then holding the chosen securities in the original
percentage of the portfolio and not changing the composition of the portfolio
- Another technique of passive portfolio management is buying shares of a market index fund that mimics a market index
(e.g., S&P/TSX Composite Index) and holding it
- Investors do not pay transaction fees for frequent buying and selling. They also do not spend a lot of time gathering
information to find underpriced securities
Active Portfolio Management
- In contrast to passive management, active management involves changing the composition of portfolios
- Some active managers follow market timing strategy. There are mutual fund managers who specialize in market timing.
This strategy involves using various techniques and predicting future movements in financial instruments, especially
stocks, and buying and selling them at the right time. Also, market timers may advocate moving into a stock market or an
industry at a particular time
- Other managers attempt to find undervalued and overvalued securities, buy the undervalued ones and short sell the
overvalued ones to try and obtain abnormal profits
- Active management is costly, time consuming, and risky. Investors need to evaluate managers of actively managed
funds to find out whether or not their strategies are successful. The Sharpe ratio, Treynor ratio, and all the other risk
measures are important tools for these investors
13.2 Performance Evaluation
- Performance Evaluation: is a term for assessing how well a money manager achieves a balance between high returns
and acceptable risks
- The raw return on a portfolio, R , is simply the total percentage return on a portfolio
- The raw return is a naive performance evaluation measure because:
> The raw return has no adjustment for risk
> The raw return is not compared to any benchmark, or standard
- Therefore, the usefulness of the raw return on a portfolio is limited
Sharpe ratio = R pR f
The Sharpe Ratio
- The Sharpe ratio a reward-to-risk ratio that focuses on total risk
- It is computed as a portfolio’s risk premium divided by the standard deviation of the portfolio’s return
Treynor ratio = p f
The Treynor Ratio
- The Treynor ratio is a reward-to-risk ratio that looks at systematic risk only
- It is computed as a portfolio’s risk premium divided by the portfolio’s beta coefficient α p R −pR + β f E Rp [ ( M) −R f]}
- Jensen’s alpha is the excess return above or below the security market line. It can be interpreted as a measure of by
how much the portfolio “beat the market.”
- It is computed as the raw portfolio return less the expected portfolio return as predicted by the CAPM
“Extra” Return = Actual Return - CAPM Risk-Adjusted ‘Predicted’ Return
Another Method to Calculate Alpha
- Recall that the characteristic line graphs the relationship between the return of an investment (on the y-axis) and the
return of the market or benchmark (on the x- axis).
- The slope of this line represents the investment’s beta.
- With only a slight modification, we can extend this approach to calculate an investment’s alpha.
- Consider the following equation,
E R P)− Rf= [E(R M)−R f]×βP
or,interms of risk premiums :
E R )= E(R )×β
P,RP M,RP P
- Suppose an
actively managed fund took on the same amount of risk as the market (i.e., a beta of 1), but the fund earned exactly 2%
more than the market every period?
- If we graph this hypothetical situation, the slope (i.e., beta) is still 1, but the x intercept is now 2. This intercept value is
the fund’s alpha. Estimating Alpha Using Regression
- Suppose we want to estimate a fund’s alpha.
- Unlike the previous situation, we do know whether its returns are consistently higher (or lower) than the market by a
- In this case, we apply a simple linear regression.
- X-variable: the excess return of the market
- Y-Variable: the excess return of the investment
- The intercept of this estimated equation is the fund’s alpha.
- Consider the following Spreadsheet Analysis slide.
- In the spreadsheet example, the intercept estimate is -.0167, or -1.67 percent per year.
- The beta of this security is .96, which is the coefficient estimate on the x variable.
How would you characterize the performance of this fund? The Information Ratio
- Suppose a mutual fund reports a positive alpha.
- How do we know whether this alpha is statistically significantly different from zero or simply represents a result of
> One way: Evaluate the significance level of the alpha estimate using a regression.
> Another way: Calculate the fund’s information ratio
- The information ratio is a fund’s alpha divided by its tracking error.
- Tracking error measures the volatility of the fund’s returns relative to its benchmark.
- Consider the fund we evaluated in the Spreadsheet Analysis in the previous slide.
> Over the five years, the excess return differences are 2%, 4%, -20%, 14%, and -10%.
> The tracking error is the standard deviation of these return differences, which is 13.2%.
> The information ratio for this fund is -1.67% divided by 13.2%, which is -0.13.
- The information ratio allows us to compare investments that have the same alpha: A higher information ratio means a
lower tracking error risk.
- Recall that correlation measures how returns for a particular security move relative to returns for another security.
Correlation also plays a key role in performance measurement.
- Suppose a particular fund has had a large alpha over the past three years.
> All else equal, we might say that this fund is a good choice.
> Suppose this fund is a sector-based fund that invests only in gold.
> It is possible that the large alpha is simply due to a run-up in gold prices over the period and is not
reflective of good management or future potential.
- To evaluate this type of risk we can calculate R-squared, which is simply the squared correlation of the fund to the
- For example, if this fund’s correlation with the market was .60, then the R-squared value is .36.
- R-squared represents the percentage of the fund’s movement that can be explained by movements in the market.
- Because correlation ranges only from -1 to +1, R-squared values will range from 0 to 100 percent.
> An R-squared of 100 indicates that all movements in the security are driven by the market, indicating a
correlation of -1 or +1.
> A high R-squared value (say greater than .80) might suggest that the performance measures (such as alpha)
are more representative of potential longer term performance.
> Excel reports correlation as “Multiple R” and R-squared as “R Square.”
- Verify that the squared value for “Multiple R” equals “R Square” in the previous Spreadsheet Analysis slide.
- M Measure gives us the excess return of a hypothetical portfolio over the market portfolio.
- For a portfolio p, we can create a hypothetical portfolio by combining a percentage of portfolio p with a risk-free asset (T-
bill) such that the hypothetical portfolio will have the same standard deviation