标题: Sharpe Ratio [打印本页] 作者: malbec 时间: 2011-7-11 19:41 标题: Sharpe Ratio
I ran through this. Didnt make much sense to me. Any help would be helpful:
'assuming all investors agree on all asset return, variance, and correlation expectations, then the market portfolio has the highest sharpe ratio"
Any idea?作者: Rasec 时间: 2011-7-11 19:41
PM is one of my weakest points, but the above seems to say that in an efficient market, the best possible return is the market's return. Any other return is not possible, so the market portfolio has the highest sharpe ratio by definition....weird, but that's how I can interpret the above statement.作者: President1988 时间: 2011-7-11 19:41
Ya.. I guess it's the only way! I hate these theory impractical questions. As if we will ever use them in real world!作者: SeanWest 时间: 2011-7-11 19:41
Sharpe ratio is return/risk, since the market portfolio is the most superior portfolio in an efficent market i.e. it has the lowest risk for a given return, all other portfolios have either a lower return for the same risk, or a higher risk for the same return, so the market portfolio will have the highest sharpe, hope this helps
Edited 1 time(s). Last edit at Monday, May 2, 2011 at 01:41PM by pedpenny.作者: tarunajwani 时间: 2011-7-11 19:41
With all the assumptions the market portfolio is the best portfolio (highest sharpe ratio, highest additional return over risk free rate for each unit of additional risk taken by means of leverage). No other combination can beat it.
Edited 1 time(s). Last edit at Monday, May 2, 2011 at 01:41PM by janardhanc.作者: Kapie 时间: 2011-7-11 19:41
While everybody seems to 'interpret' sharpe ratio, nobody has answered the fundamental question - why market portfolio has the highest sharpe ratio!
Here are some additional thoughts:
1. There are infinite number of portfolios with the same Sharpe ratio as the market porfolio.
2. These portfolios all have market portfolio in them
What are these portfolios? To fundamentally understand this - ask yourself, what is 'market' portfolio?
The market portfolio is every security in the world. If every asset is fairly priced (sits on SML line), then each one provides the correct amount of return for the correct amount of risk. Plus, each security added provides incremental diversification benefit (lowers the volatility).
1) Removing assets with returns higher than the market portfolio would lower the return & increase the volatility by decreasing diversification (lower Sharpe).
2) Removing assets with returns lower than the market portfolio would increase returns, but increase the volatility of the portfolio by a great amount (again, lower Sharpe).
If you don't believe this, then rework the table on page 154 of Schweser, Book 5 by hand. Or look at figure 1 on page 150. Both illustrate the math involved, on a smaller scale.
"1. There are infinite number of portfolios with the same Sharpe ratio as the market porfolio."
Just reference page 162 of book five. Again, it may not be intuitive, but that's how the math works out. As you change the mix of the market portfolio and the rf asset, the volatility of the portfolio and the expected return both increase and decrease linearly. For each additional % of return added, volatility increases proportionally, thus the Sharpe ratio will remain constant.
"2. These portfolios all have market portfolio in them"
You are essentially dialing the risk and return of the market portfolio up and down by mixing in the rf asset.
