The Sharpe Ratio: How Risk Adjusted Return Makes You Money

A recent column by Trent over at The Simple Dollar debated the merits of saving for retirement versus paying down debt.  I have also written previously on the subject of paying down debt and how I received a guaranteed 8% Return on my investment, prompting further discussion of this topic.

Why even write this article? Everyone knows they should be paying down debt and saving for retirement simultaneously…or should they?

Let’s take a look.

The Math

When we are investing for retirement we will eventually have to pay tax on the invested funds and the gains made by those investments (unless we invest in a Roth IRA).

The previous point is the key because paying down debt provides us with an absolute guaranteed return equal to the amount of the interest rate we are paying on the loan. Conversely, investing for retirement requires that tax be paid on the money when the investment is cashed in or withdrawn from a sheltered account.

Simply put, this means that we must achieve a pre-tax return on investment (ROI) that exceeds the interest paid on debt by the amount that the investment return will be taxed.

Adjust The Return For Risk

In addition to having to exceed the rate of return offered by paying down debt, the investment must also be adjusted for the additional risk that you are taking on by choosing to invest in stocks etc. versus the “risk free rate” of paying down debt.

The risk free rate is typically defined as the rate that is currently paid on 90-day US Treasury bonds. However, repayment of debt is also risk free at the rate of interest paid on the debt.

A typical measure of Risk vs. Reward is the Sharpe Ratio. Typically speaking the higher the Sharpe Ratio the greater the return for the same amount of risk. Of course, when there is virtually no risk, as in debt repayment or 90-Day treasury bonds, then there is no variability of returns and the Sharpe ratio will not apply.

Calculating the Sharpe Ratio

Suppose the asset has an expected return of 15% in excess of the risk free rate. We typically do not know the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset’s excess return, as 10%.

The risk-free return is constant.

Then the Sharpe ratio (using a new definition) will be 1.5 (R = 0.15 and ? = 0.10).

As a guide post, one could substitute in the longer term return of the S&P500 as 10%. Assume the risk-free return is 3.5%. And the average standard deviation of the S&P500 is about 16%.

Doing the math, we get that the average, long-term Sharpe ratio of the US market is about 0.40625 ((10%-3.5%)/16%).

But we should note that if one were to calculate the ratio over, for example, three-year rolling periods, then the Sharpe ratio would vary dramatically.

What Does This All Mean?

I strongly urge that when you review your asset allocation that you take a look at the amount of money that you allocate to fixed income investments.

Why just fixed income?

Fixed income investments, such as bonds, are the closest thing that is comparable to one’s debt or more specifically a mortgage.

In light of the risk adjusted return calculations, it is possible to get an acceptable return on investments in equities but highly unlikely that an investment in bonds or other fixed income that could beat the return  (especially after tax) from paying down debt.

Because of this, I highly encourage investors with outstanding debt (including a mortgage) to consider allocating the “fixed income” portion of their portfolio to reducing debt.  It makes sense mathematically, it helps improve your credit score and it feels good to know that your debt is being reduced more quickly than originally planned.

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