Advisor Blog

It is axiomatic in the world of financial economics that, in capital markets, risk and return are always related.  In fact, you will often hear that in order to create a portfolio with a higher expected rate of return, one must take additional risk.  One of my friends, who is also a client, recently told me that this seemingly obvious statement is very confusing to a lot of people.  He asked me how this could be true when a comparing a poorly diversified portfolio with a well diversified one.  And, he has a point.

The statement assumes that idiosyncratic risk in the portfolio has already been diversified away.  After that, adding to expected return requires taking more market risk.  Understanding the difference between indiosyncratic (or non-systematic) risk and market (or systematic) risk is critical to understanding this concept.  And, unless you've taken some finance courses or you're a portfolio manager (not a product salesman at a brokerage firm), you may not fully understand this.

Idiosycnratic, or non-systematic risk is risk that can be diversified away in a portfolio.  This is risk associated with individual assets.  An example would be company risk associated with an individual stock position (think Enron, for example).  If you hold just a few stocks in your portfolio, this is very signficant.  If you hold a few thousand stocks, it is so insignificant that it's close to zero.  It has been "diversified away".  The Capital Asset Pricing Model (CAPM) for which Sharpe won the Nobel Prize tells us that investors are not compensated for taking diversifiable (idiosyncratic or non-systematic) risk.  In other words, investors are only compensated for bearing market risk.

Market risk is risk that cannot be diversified away.  Rational investors eliminate all diversifiable risk for which they should not expect to be compensated.  Now, we can examine the statement that higher expected returns require taking additional risk.  The assumption is that diversifiable risk has been taken out of the equation.  Thus, tilting a portfolio toward riskier asset classes like small cap or value stocks increases the expected rate of return.  Likewise, adding less risky assets such as bonds, to the portfolio will reduce the expected rate of return.  Of course, this also reduces the overall risk in the portfolio and is used to adjust the level of portfolio risk to a level that is suitable for a client's risk tolerance, capacity, and time horizon.

The concept is better explained by the statement that, in a properly diversified portfolio, additional expected return can only be achieved by taking additional market risk.

In a discussion with Scott Maxwell yesterday about fixed income choices for the portfolio of one of his clients, we found that we made frequent references to the Sharpe Ratio of the fixed income funds and the portfolio design. This lead us to wonder how many clients or prospective clients really understand this important risk/return measurement.

The Sharpe Ratio is named after William Sharpe, winner of the Nobel Memorial Prize in Economic Sciences for his work on the Capital Asset Pricing Model (CAPM - more about that in a future post). The ratio describes how much excess return is generated by a portfolio in exchange for the additional volatility of the portfolio that the investor must endure. The point is that an investor must be properly compensated for bearing additional risk beyond that of a risk-free asset.

S(x) = (rx-Rf) / std dev (x)

This formula describes the calculation where the Sharpe Ratio of the portfolio is equal to the average rate of return for the portfolio minus the risk free rate of return (usually short-term T-bills) divided by the standard deviation of the portfolio.

Why is this so important? Because it describes the efficiency of the portfolio - how much return is generated for each unit of risk taken. Obviously, a higher number is better. This allows us to compare the performance of a portfolio to another that takes more or less risk. It also allows us to maximize the efficiency of portfolio designs.

Consider two portfolios with identical returns. One is riskier than the other. A rational investor would always choose the least risky portfolio with the same return. Conversely, consider two portfolios with identical risk. One has a higher return. A rational investor would always choose the portfolio with the highest return. The Sharpe Ratio provides a method for calculating this risk/return tradeoff.