## Sharpe Ratio and Leverage

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assumer
Posts: 432
Joined: Fri Dec 21, 2012 11:11 pm

### Sharpe Ratio and Leverage

It seems to me that a rational thing to maximize in a portfolio is the Sharpe ratio (mean divided by standard deviation). Let us assume that Investment A has a higher Sharpe ratio than Investment B but a lower mean. I've heard it state that "leverage" can bring up the mean, or somehow normalize this. In my understanding leverage is simply borrowing to invest. My questions are:

1. How does the interest rate on the borrowed money affect the Sharpe ratio?
2. How do/could institutional investors (e.g. hedge funds, pensions) employ leverage?
3. How do/could retail investors (e.g. average Joe and Jane) employ leverage?

magician
Posts: 1566
Joined: Mon May 02, 2011 1:08 am
Location: Yorba Linda, CA
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### Re: Sharpe Ratio and Leverage

assumer wrote:It seems to me that a rational thing to maximize in a portfolio is the Sharpe ratio (mean divided by standard deviation)
The Sharpe ratio is not the mean (return) divided by the standard deviation (of returns); the numerator is the mean return minus the risk-free rate. Maximizing the Sharpe ratio is one approach to deciding the asset mix in one's portfolio, but it is not the only one. A lot depends on the risk aversion of the investor.
assumer wrote:Let us assume that Investment A has a higher Sharpe ratio than Investment B but a lower mean [return]. I've heard it state that "leverage" can bring up the mean, or somehow normalize this. In my understanding leverage is simply borrowing to invest.
Yes, by borrowing (at a rate less than the return on your investment) you can increase the overall return.
assumer wrote:My questions are:

1. How does the interest rate on the borrowed money affect the Sharpe ratio?
If you can borrow at the risk-free rate, the Sharpe ratio of the leveraged portfolio will be the same as the Sharpe ratio of the unleveraged portfolio. If, in the more likely case, the rate at which you can borrow is higher than the risk-free rate, the Sharpe ratio of the leveraged portfolio will be lower than the Sharpe ratio of the unleveraged portfolio.
assumer wrote:2. How do/could institutional investors (e.g. hedge funds, pensions) employ leverage?
They can do it by borrowing money (e.g., buying on margin), or by using various derivative securities (e.g., futures or forwards).
assumer wrote:3. How do/could retail investors (e.g. average Joe and Jane) employ leverage?
Buying on margin or entering into futures contracts would probably be the simplest way.

Note: that isn't intended as an endorsement of these investments.
Simplify the complicated side; don't complify the simplicated side.

Akiva
Posts: 534
Joined: Tue Feb 15, 2011 2:33 pm

### Re: Sharpe Ratio and Leverage

assumer wrote:It seems to me that a rational thing to maximize in a portfolio is the Sharpe ratio (mean divided by standard deviation). Let us assume that Investment A has a higher Sharpe ratio than Investment B but a lower mean. I've heard it state that "leverage" can bring up the mean, or somehow normalize this. In my understanding leverage is simply borrowing to invest. My questions are:

1. How does the interest rate on the borrowed money affect the Sharpe ratio?
The embedded interest rate on futures and options is very competitive. Furthermore, with futures, you can put the money you don't need for margin (i.e. almost all of it) in a money market account and earn interest to offset the embedded interest on the futures contract. This leaves you only very slightly worse off than a cash position. (10 basis points or so).
2. How do/could institutional investors (e.g. hedge funds, pensions) employ leverage?
3. How do/could retail investors (e.g. average Joe and Jane) employ leverage?
The two ways a normal investor would get leverage are either buy taking a futures position or by buying deep in the money calls. Stay away from those leveraged ETFs because they only track the index on a daily basis and do not work for longer time horizons.

These are the preferred means for institutional investors. But they also have the option of borrowing money at rates close to those embedded in futures and options and then just doing the trades with the borrowed money.