13. Performance Evaluation and Risk Management. It is Not the Return On My Investment. “It is not the return on my investment that I am concerned about. It is the return of my investment!”. – Will Rogers. However,. “We’ll GUARANTEE you a 25% return of your investment!”.
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Performance Evaluation and Risk Management
“It is not the return on my investment
that I am concerned about.
It is the return of my investment!”
– Will Rogers
“We’ll GUARANTEE you a 25% return of your investment!”
–Tom and Ray Magliozzi
To get a high evaluation of your investments’ performance, make sure you know:
1. How to calculate the three best-known portfolio evaluation measures.
2. The strengths and weaknesses of these three portfolio evaluation measures.
3. How to calculate a Sharpe-optimal portfolio.
4. How to calculate and interpret Value-at-Risk.
The Sharpe Ratio
The Treynor Ratio
CAPM Risk-Adjusted ‘Predicted’ Return
Treynor ratio and Jensen’s alpha:
Standard deviationSharpe-Optimal Portfolios, I.
Standard deviationSharpe-Optimal Portfolios, II.
So, now our job is to choose the weight in asset S that maximizes the Sharpe Ratio.
We could use calculus to do this, or we could use Excel.
Suppose we enter the data (highlighted in yellow) into a spreadsheet.
We “guess” that Xs = 0.25 is a “good” portfolio.
Using formulas for portfolio return and standard deviation, we compute Expected Return, Standard Deviation, and a Sharpe Ratio:
Well, the “guess” of 0.25 was a tad low….
Prob(13 – 20 RS&P500 13 + 20) 0.67
or Prob (–7 RS&P500 33) 0.67
13 + 13 = 26%
400 + 400 = 800.
Prob(26 – 228 RS&P500 26 + 228) .95
orProb (–30 RS&P500 82) .95
Using the procedure from before, we make make probability statements. Three very useful ones are: