This document discusses various methods for evaluating investment performance, including return, risk, and risk-adjusted performance measures. It describes calculating total return as the change in wealth over a period, and measuring total risk as the standard deviation of returns. Risk-adjusted measures discussed include the Sharpe and Treynor ratios, with the Sharpe ratio using total risk and the Treynor using only systematic market risk. The document also covers measuring diversification through correlation to the market and Jensen's Alpha for determining manager performance beyond market returns.

1. Evaluation of Investment
Performance
Chapter 22
Charles P. Jones, Investments: Analysis and Management
22-1

2. How Should Portfolio
Performance Be Evaluated?
• “Bottom line” issue in investing
• Is the return after all expenses adequate
compensation for the risk?
• What changes should be made if the
compensation is too small?
• Performance must be evaluated before answering
these questions
22-2

3. Considerations
• Without knowledge of risks taken, little can be
said about performance
– Intelligent decisions require an evaluation of risk and
return
– Risk-adjusted performance best
• Relative performance comparisons
– Benchmark portfolio must be legitimate alternative
that reflects objectives
22-3

4. Return Measures
• Change in investor’s total wealth over an
evaluation period
(VE - VB) / VB
VE =ending portfolio value
VB =beginning portfolio value
• Assumes no funds added or withdrawn during
evaluation period
– If not, timing of flows important
22-4

5. Risk Measures
• Risk differences cause portfolios to respond
differently to market changes
• Total risk measured by the standard deviation of
portfolio returns
• Nondiversifiable risk measured by a security’s
beta
– Estimates may vary, be unstable, and change over time
22-5

6. Risk-Adjusted Performance
• The Sharpe reward-to-variability ratio
– Benchmark based on the ex post capital market line
– =Average excess return / total risk
– Risk premium per unit of risk
– The higher, the better the performance
– Provides a ranking measure for portfolios
22-6
 /SD
RF
TR
RVAR p
p 


7. Risk-Adjusted Performance
• The Treynor reward-to-volatilty ratio
– Distinguishes between total and systematic risk
– =Average excess return / market risk
– Risk premium per unit of market risk
– The higher, the better the performance
– Implies a diversified portfolio
22-7
 /β
RF
TR
RVOL p
p 


8. RVAR or RVOL?
• Depends on the definition of risk
– If total (systematic) risk best, use RVAR (RVOL)
– If portfolios perfectly diversified, rankings based on
either RVAR or RVOL are the same
– Differences in diversification cause ranking differences
• RVAR captures portfolio diversification
22-8

9. Measuring Diversification
• How correlated are portfolio’s returns to
market portfolio?
– R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
– R2 is the coefficient of determination
– Excess return form of characteristic line
– The lower the R2, the greater the diversifiable risk
and the less diversified
22-9

10. Jensen’s Alpha
• The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
– CAPM implies a is zero
– Measures contribution of portfolio manager beyond return
attributable to risk
• If a >0 (<0,=0), performance superior (inferior, equals) to
market, risk-adjusted
22-10

11. Measurement Problems
• Performance measures based on CAPM and its
assumptions
– Riskless borrowing?
– What should market proxy be?
• If not efficient, benchmark error
• Global investing increases problem
• How long an evaluation period?
– AMIR stipulates a 10 year period
22-11