Since the fall of 2019, BCC’s financial planning Core Curriculum classes have adjusted to include all content from the FP Canada Institute™ Financial Planning Body of Knowledge (FP-BoK). The FP-BoK is a robust attempt to describe all the technical knowledge required of a financial planning professional. The FP-BoK includes the following note about Sharpe Ratios:
- Define measurements of risk-adjusted return, such as:
- Sharpe Ratio
- Treynor Ratio
- Jensen Index
- Identify when the use of each measurement of risk-adjusted return is appropriate.
- Explain each of the measurements of risk-adjusted return.
- Interpret each of the measurements of risk-adjusted return.
For the purpose of this article, we will focus only on the Sharpe Ratio. The Treynor Ratio and Jensen Index are useful as more targeted measures of risk-adjusted return. The Body of Knowledge can be found at https://www.fpcanada.ca/en/bok/bok-statement?topicUrl=investments&articleUrl=measurement-of-risk-adjusted-return
For starters, let’s explore the concept of risk-adjusted return. To examine this, we’ll use the example of the classic dice game Yahtzee. My wife and I often play Yahtzee while we dine together, and it’s an excellent example of a combination of luck and understanding of statistics. For those unfamiliar with the game, the point is to roll what are essentially poker hands (straights and 3, 4, or 5-of-a-kinds) on 5 dice, given 3 opportunities to do so. At the end of each roll, the player sets aside dice that will contribute towards their final ‘hand’ and re-rerolls the rest.
In this example, we’ll deal with a common conundrum in the game. Let’s say our player rolls a full house on their first roll, rolling 3 fives and 2 twos. This hand scores 25 points if the player chooses to take it. We’ll call this bet the sure thing. But let’s say this player is willing to take a chance. They know that 3 fives they have rolled is useful, so that person picks up their 2 twos and attempts to roll a fourth five (potentially scoring a 4-of-a-kind) or, better yet, two more 5s, scoring a 50-point Yahtzee. The chance of rolling a Yahtzee at this point is about 1.26%, which means this should happen about 1 of every 80 times a player takes this gamble. (Yahtzee stats are fully explored at https://www.thoughtco.com/probability-of-rolling-a-yahtzee-3126593)
Let’s say that the player happens to succeed at this gamble, and rolls 2 more fives, obtaining their Yahtzee. This player will likely feel that their gamble was a good gamble and their risk-taking paid off. The player sacrificed a sure 25 points for a risky 50 points, doubling their payoff. How much additional risk did the player take to obtain their ‘return’ in this case?
That is essentially what we are measuring with the Sharpe ratio. Rather than focus on the return generated by an investment decision, Sharpe is intended to explore whether the decision that led to the return was a good decision. This allows us to explore a decision based on its process rather than its outcome. A higher Sharpe ratio is preferable, as it indicates more return generated per unit of risk
taken. This relies on the premise that we should only take risk to generate returns. In our Yahtzee example above the player who gambles for a Yahtzee will have a lower Sharpe ratio than the player who takes the full house, representing a riskier decision, even though the outcome may have been superior.