# What is the Jensen, Sharpe, and Treynor ratios?

CERTIFIED FINANCIAL PLANNER® (CFP) professionals and QUALIFIED ASSOCIATE FINANCIAL PLANNER™ (QAFP) professionals are expected to understand how to properly advise their clients on investments, including risk-adjusted returns. A risk-adjusted return is the calculation of profit (the return) that an investment could make while considering the degree of risk that the investor must accept to get that profit.

Investors and investment professionals can understand the risk factor associated with an investment is to use the Sharpe Ratio, Treynor Ratio or Jensen Index, or a combination of all three. The goal of each of these ratios is to combine the potential risk and performance of an investment portfolio into a single value. A savvy investment professional should be able to take a look at a client’s investment portfolio and based on what’s in it, use an appropriate risk-adjusted return calculation to determine the client portfolio’s potential return. Since each of these ratios are based on different investment philosophies, let’s take a look at the definition of each.

## Sharpe Ratio

The Sharpe Ratio was created by William F. Sharpe, an American economist who won the Nobel Prize in Economics in 1990. The purpose of the Sharpe ratio is to explore whether the amount of risk that led to a return was worth it. In other words, it focuses on the journey rather than the outcome, relying on the premise that risk is needed in investments to generate a return. In its equation, the Sharpe Ratio focuses on the standard deviation calculation to determine the total risk and return for a portfolio.

Keeping in mind the definition of a risk-adjusted return, let’s take a look at a simple example of the Sharpe Ratio in action with the game Yahtzee, focusing on the idea that just because a portfolio gets a higher return, it might not be worth the amount of risk that was needed to get that return.

For context, Yahtzee is a game that is played with 5 regular 6-sided dice and a cup. The object of the game is to get the highest score possible within three turns. On the first turn, the player places all 5 dice in the cup and shakes it, pouring out the five dice. The player can then set any dice they want to keep to the side. For the second and third turns, the player can roll any of the dice from any previous roll. On the third turn, the player calculates their final score. A game of Yahtzee consists of thirteen rounds, but for this example, we’re just going to focus on the fact that the highest score you can get in one turn is 50 points, which is referred to as a Yahtzee.

Let’s say a player rolls a full house on their first roll which is 3 fives and 2 twos. This hand scores 25 points if the player chooses to take it, which is a good score. But let’s say this player is willing to take a chance to get an even better score to secure their victory. They know that the 3 fives they have rolled are 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.

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?

Whether the risk that the player took to get their high score was worth it is subjective, but considering the 1.26% chance of rolling a Yahtzee, it seems the safer decision would be to keep the score of 25 for the turn.

## Treynor Ratio

The Treynor Ratio is very similar to the Sharpe Ratio, where it considers the amount of risk needed to get a return. In its equation, the Treynor Ratio focuses on the Beta calculation to determine the diversifiable risk for a portfolio. Therefore, the Treynor Ratio would best be used to determine the potential performance of diverse investment portfolios.

## Jensen Index

The Jensen Index, also known as Jensen Measure or Jensen Alpha, is a calculation that measures the excess returns of a portfolio compared to the suggested returns by the Capital Asset Pricing Model (CAPM). In other words, The Jensen measure uses “alpha” to calculate the difference between the actual return and the return that the CAPM predicted.

The CAPM considers two types of risk:

• Systemic risk, which refers to general market risks. These risks are inherent and can’t be avoided, such as interest rates.
• Unsystemic risk, also known as specific risk, which relates to individual stocks.

Unsystemic risk can be mitigated through a diversified portfolio, but a diversified portfolio doesn’t solve the problem of systemic risk. Therefore, the CAPM evolved to calculate systemic risk for a portfolio, so an investor at least knows what they are dealing with.

## Investment risk

Calculating investment risk and giving good investment advice to clients can be difficult. Careful attention to the different measurement tools available and being able to choose the best single tool or a combination of tools to calculate risk for your client is just one part of being a great Certified Financial Planner® (CFP®) and a Qualified Associate Financial Planner (QAFP™) professional. Consider taking our comprehensive BCC program with live instruction options to enhance your learning today.