The asset management industry uses a variety of "performance measures" to asses the relative performance of managed portfolios or funds, mostly (but not always) relative to an appropriate benchmark. One such measure, the "Sharpe ratio", was introduced in the  lectures. The "Treynor ratio" is defined in very much the same way, with the only exception that the denominator is not the portfolio's volatility ("sigma"), but instead it's  "beta" (i.e. the slope coefficient in a CAPM-style regression of portfolio returns onto a benchmark). Another performance measure used frequently is "alpha" (the intercept in the aforementioned regression). There are other measures (e.g. "M2" or the "Information  Ratio"); feel free to include any of these in your discussion at your discretion.

(a) Provide a discussion of the characteristics of these performance measures (and any others you may choose to include). Discuss in particular:

• What exactly is being measured?
• How does the measure account for risk (and what kind of risk)?
• What are the differences between the measures?

(b) Discuss what performance measure(s) you would employ (and why?) if you were any of the following:

• The manager of a "fund of funds", selecting a portfolio of funds.
• A "high-net-worth" individual choosing a hedge fund to invest in.
• An individual choosing a pension fund to invest their life savings.

(c) Below are two statements that we found in articles on performance measures.

Chose either one of these statements and provide a brief discussion:

 Statement (1):

 Investors use performance measures to decide where to drop their money. But clearly, since very few of us can see into the future, we are constrained to using historical (past) data to compute those measures. But investors probably do not care about how much they would have made if they had invested in the fund in the past, but how much they will make in the future if they invest now. The question is thus, how much does past performance tell us about future performance? Based on the empirical evidence, the answer seems to be: very little!