**Leveraging Your Portfolio**

Traditionally, most advisors suggest that young investors start with a portfolio consisting of 80-90% equities and 10-20% fixed income. As the investor approaches retirement, heshould shift the mix to a larger portion of fixed income to reduce the variance of the annual returns and generate more interest income for spending. The investor’s initial portfolio is described as "aggressive" because of its low proportion of lower variance fixed income assets.

However, some investors may have a higher tolerance to risk and may be interested in constructing a more aggressive portfolio. One way of accomplishing this is to leverage your portfolio by borrowing money and eliminating the fixed income component of your portfolio. For example, if you had $10,000 to invest, you could decide to borrow $5,000 and then invest the total $15,000 in all equities. This approach could enhance the returns that you earn. Hopefully, the equity return levels on the borrowed money will more than enough to cover the required interest payments.

However, leveraging your portfolio will introduce more risk. The swings in your portfolio’s value due to varying year-to-year returns will now occur on a larger amount of capital. Since some of this capital is borrowed money, there is a chance for default if your portfolio value drops too severely. However, you may be willing to accept this increased risk if the returns will be higher with a leveraged account.

One key issue is to identify a loan provider for the portfolio leverage. There are actually many options but the interest rates will vary greatly. You could consider obtaining a loan from a bank – either a home equity loan (if you own a house) or a personal loan. The interest rates on personal loans can be high if it is unsecured. Another option to consider is to open a margin account with a brokerage and trade from that account. The securities that you are trading will provide the collateral for the margin loan. This is the easiest option to implement for an individual investor.

For most investors, we feel that leveraging your portfolio will not prove to be a prudent strategy. The key challenge for an individual investor is to borrow money at a competitive interest rate. For instance, the long term real returns from U.S. equities are about 7%. The real interest rate has averaged about 3% (that’s the average yield for a 10 year Treasury bond). Now, since the individual’s credit is not as good as the U.S. government’s credit, they will be charged a premium above this 3% interest rate. This will probably be at least 2.5%. Currently, eTrade allows investors to trade on the margin at a price about 2.5% above the 10 year bond yield if the investor has an account value more than $1m. The interest rate increases for smaller investors. So, the investor’s net additional return on borrowed money will be about 1.5%. If the investor is only planning to remain in a leveraged position for 10 years or so, the extra 1.5% return is useful but not so dramatic that it will massively change your returns. However, the investor will be taking on more risk – potentially leading to some sleepless nights in a bear market.

In the next section, we will perform some analysis based on historical data to give an idea of the potential gain in return and the associated increase in risk.

**Data Analysis**

**Data Analysis**

To develop some quantitative assessments of the impact of leverage, we have modeled actual returns from historical data for various degrees of leverage. Our model is based on an investor starting with a certain level of leverage (50% for instance) and gradually reducing the leverage to 0% over a 10 year period. We think this makes sense as some investors may want to have leverage from the ages of 25 to 35. By the time they reach the age of 35, the investor would like to have a portfolio with no debt.

We have examined 5 different levels of leverage (no leverage, initial 25% leverage, initial 50% leverage, initial 100% leverage, and initial 200% leverage). When the investor has some leverage, we assume that he pays interest at a rate 2.5% higher than the 10 year Treasury bond yield at the beginning of the 10 year period. At the end of each year, the investor will pay interest on his outstanding debt and pay down 10% of the principal. Thus, at the end of the 10 years, there will be no debt outstanding.

The equities that will be invested in are the S&P 500 index. We have studied 44 ten-year periods beginning in 1952. We compare the internal rates of return (IRR) for the 10 year period.

Here is a summary of the results:

As expected, we see an increase in the 10 year mean IRR as the amount of leverage increases. However, the increase is relatively small – about 0.5% for the 100% leverage case. The 10 year standard deviation of the IRR is relatively small (this is expected as the variance in stock returns rapidly diminishes as the time horizon increases) but does substantially increase as leverage is added. We do see that leverage will produce more periods when the IRR surpasses 20%. Unfortunately, it will also produce more poor performing periods.

To give the investor a better sense of the increase of volatility in his portfolio that the additional leverage will cause, we have calculated the standard deviation of the annual changes of the un-leveraged portion of his portfolio. The un-leveraged portion represents the total portfolio value minus the outstanding debt. The annual standard deviation in returns is somewhat large in the un-leveraged case (16%) and rises to 25% when the investor is 100% leveraged. Above 100% leverage, the standard deviation becomes massive. We believe this standard deviation is a key figure for the investor. It will give an indication of how much the value of his portfolio will fluctuate on an annual basis. High fluctuations can cause an investor to lose nerve and switch strategies in the middle of an investment period which will probably do more harm than good.

The investor needs to ask himself the question: Can he handle a standard deviation of 20% or 25%? A 25% standard deviation generally means that about 18% of all years will see a loss of at least 13% of the portfolio’s value. About 3% of all years will see a drop of at least 38%.

**Discussion**

**Discussion**

In our opinion, the increase in standard deviation seems substantial in comparison to the gain in mean IRR. Especially since we are assuming that the investor will only gain this additional return for a period of 10 years. The difference in eventual value of $100,000 invested at 12% vs. 11.5% annual returns over 10 years is only about $14,000 ($310,000 vs. $296,000). Young, aggressive investors may disagree – but we’ll take more restful nights of sleep over an extra $14,000.

One factor that could have a major change to our results would be the availability of cheaper capital. If the investor has a lending source that charges a rate closer to a Treasury bond, then the leverage will be more advantageous.

Two professors from Yale’s Law School have performed a similar analysis with a more aggressive use of leverage. They are more aggressive in their use of leverage both in terms of starting at a higher amount of leverage (200%) and maintaining a leveraged position for a longer period of time. Additionally, their analysis assumes continuing contributions from the investor rather than just considering the leverage on an existing portfolio. They also use a set of data which reflects a longer time period (with investments beginning in 1850). Their results argue for using leverage to avoid possibly bad outcomes. Their article is called Mortgage your Retirement.