## Understanding Management’s Value

You would like to evaluate a potential portfolio manager. Is s/he any good? How do you know?

Most people would look at the manager’s performance and compare it to other managers and an index. Many would look at some rating service to see how many ‘stars’ the manager had (too bad they don’t know how those calculations are weighted and their complete lack of predictability, but that’s another article).

Does ANY of that really tell you how good the manager actually is?

The real question is whether the manager actually *added value *to the underlying portfolio holdings. After all, a manager is being paid to *manage*! What if the portfolio holdings would have done just as well – or better – if left unmanaged completely?

Knowing whether the manager actually adds value is an important part of the management selection process.

Do you have your green eye-shades ready? A little warning: There’s math involved.

Before a manager’s value can be understood, a portfolio’s *expected* return must be identified. For this, we use the **Capital Asset Pricing Model (CAPM)**:

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**R _{P} = R_{F} + (R_{M}-R_{F}) β_{p}**

Translation: The Expected Return of the portfolio = risk-free rate of return* + (expected return of the market minus the risk-free rate of return**) times the portfolio’s beta.

* the short-term treasury is the typical proxy.

** this is the market’s return `spread’ in excess of the risk-free rate

Is it time for a break yet?

Okay, once we know what a portfolio’s *expected* return is. We can compute the management’s alpha – a measure of added value – by analyzing actual performance.

The **Jensen Alpha** calculation is accomplished by simply using the original ‘expected return’ we found previously and subtracting CAPM. If an investment portfolio or fund generates a return that is exactly what would be expected of a portfolio or fund with its beta, the alpha would be zero. There’s no added value.

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**a _{P = }R_{P} – [R_{F} + (R_{M}-R_{F}) β_{p}]**

Once a manager’s alpha is identified, the next question generally turns to risk, i.e., how much return is achieved *per unit of risk assumed*? That’s an important question! Why would you want to assume two units of risk for one unit of return?

For this answer, one of two ratios can be used, depending on the character of the portfolio:

- The
**Sharpe Ratio**, sometimes called the*reward to variability ratio*, calculates this for undiversified portfolios using total risk. The **Traynor ratio**, sometimes called the*reward to volatility ratio*, calculates this for diversified portfolios using market risk.

Each is calculated subtracting the risk-free rate of return from the portfolio’s expected return. Sharp divides the answer by the portfolio’s standard deviation. Traynor divides the answer by the portfolio’s beta.

If you’ve even read this far it shows you are either very good at mathematical analysis or you really have nothing else to read. Either way, this is probably a good place to end this before we have to call 911.

One final note: Managers are generally evaluated using *time-weighted* returns which gives each period in time the same weight, regardless of the dollars invested. Individual investors should compute their own returns using *dollar-weighted* returns if they are making additions or taking withdrawals from a portfolio. In those cases, investor performance will likely differ from the manager’s. I knew that would cheer you up.