Some people view leverage as a four letter word, especially since the market collapse in 2008/2009. But leverage, when used properly can be sensible. Heres an example use.

This is a hypothetical example based on historical data. Past performance is no guarantee of future performance. I am not an investment advisor. Do not use leverage without careful consideration and consultation with an investment professional.

Having said that, there are appropriate uses of leverage that are not high risk in the way that many people believe. Ill carry you through such an example in this article.

What leverage is

There are several ways you might use leverage in your investing practice. One is the use of options. Options are leveraged with regard to the underlying stock because a $1 move in the price of the stock often results in a movement several times larger for the option. Another is the use of margin. This article is about the use of margin.

Margin for leverage can be scary. Your brokerage will be happy to lend you money on margin. You should be sure to find out their interest rates.

If you have a margin account with a brokerage you are able to borrow money to invest in securities. A typical use of margin leverage is to purchase more shares of a stock than you could purchase without margin. As an example, if you have a $100K account, you could purchase $200K of stock. This would be 2X leverage. Your cash balance in that case would be -$100K and youd have to pay interest on that $100K.

With that account you would profit 2X times as much if the stock goes up (and lose 2X as much if it goes down). So there are risks. Heres a definition of margin from investopedia :

Buying with borrowed money can be extremely risky because both gains and losses are amplified. That is, while the potential for greater profit exists, this comes at a hefty price the potential for greater losses. Margin also subjects the investor to a number of unique risks such as interest payments for use of the borrowed money.

Sounds pretty scary doesnt it?  One reason for the scare tactics is that many an investor has gone down in flames using margin and nobody wants to see this happen to anyone again. But these outcomes are most often the result of someone using leverage to purchase volatile securities. Lets examine its use with low volatility securities.

Where leverage makes sense: To amplify high Sharpe Ratio investments

S&P 500 (blue) versus unleveraged BOND (red). March 2012 to May 2013.

Ive shown the chart at right to a number investors and asked them which portfolio is best? The blue line is the performance of the S&P 500 and the red line reflects the performance of BOND, an ETF managed by PIMCO. A lot of folks reply that they prefer the S&P 500 because its total return is higher.

Wow! People are not considering risk enough in their consideration.  Risk is typically measured in terms of volatility, or how much the securitys price moves up and down. I use daily volatility in my work. In this case, obviously, SP500 is much more volatile than BOND. On the other hand, in terms of total return, SP500 has outperformed BOND.

Measuring Risk Adjusted Return using Sharpe Ratio

Sophisticated investors realize that BONDs performance (red line) is much stronger than the S&P 500. But how can we measure that? The Sharpe Ratio was created for just this purpose. It is simply the average daily return divided by the daily volatility. All else being equal, securities with higher return have higher Sharpe Ratios, and those with lower volatility have higher Sharpe Ratios as well.

In this example, the S&P 500 has a Sharpe Ratio of 1.29, while BOND has a Ratio of 4.32.

How to take advantage of Sharpe Ratio using leverage

Many folks would assert, still, that S&P 500 is better because it provided a 20% return compared to BONDs 17%. What if we could adjust the BOND portfolio so that it outperforms the S&P (in terms of return) while still providing low volatility? Thats easy to do with margin-based leverage. Lets leverage our BOND portfolio 2X.

S&P 500 (blue) versus BOND (red) versus BOND at 2x leverage (green).

See the chart at right. Our leveraged portfolio now returns 27% compared to 20% for the S&P and 17% for the unleveraged portfolio.

How did we accomplish that? We used 2X leverage: Assume a $100K portfolio. We start by purchasing $100K of BOND, then we buy another $100K of BOND. Our cash balance is now -$100K, which well have to pay interest on, but we own $200K worth of BOND, and we reap all the returns on that. Note: 3X leverage would entail $300K BOND and a -$200K cash balance.

As long as the additional returns we receive with the leveraged portfolio are higher than our interest rate, we will benefit from the leveraged position.

The result of 2X leverage in this case is a portfolio that significantly outperforms the S&P 500 in terms of risk , return, and Sharpe Ratio. Without leverage we would not have outperformed in terms of return. Thats great, but read on, the next section is important.

A bit more detail on the math: The importance of margin rate

Brokers vary significantly in the rate they charge to borrow on margin. The broker I use (Interactive Brokers) currently charges 1.66%. That rate is built into the charts I show above. As far as I know this is the lowest rate available to a retail investor. Many, perhaps most, other brokers charge 6.00% or more. (Opinion: That is a total rip!)

The effect of a higher margin rate on the portfolio. Note the path of the green line (portfolio) compared to the chart above.

In general, we compute the daily return for our portfolio as:

• daily return =  return + (leverage 1.0) * (return (interest rate * (leverage 1.0)))

Sorry if that looks complicated. The basic idea is that our first 1X of leverage (really not leverage) is free. Then each additional 1X we have to pay interest on, and therefore reduces our daily return.

See the the chart at right. The green line (portfolio) reflects the performance of the portfolio at 2X leverage and 6% interest. We do benefit somewhat from the leverage in terms of total return (19% with leverage, 14% without). The problem is that our Sharpe Ratio is cut 33%, from 4.32 to 2.88 when compared to the lower interest rate.

It could make sense to lever up low volatility portfolios to reap higher cumulative returns. However, this only makes sense in the context of low margin rates applied to low volatility portfolios.

Tucker Balch manages a fund with a long position in BOND.