Level 1 CFA® Exam:
Performance Appraisal

Last updated: January 10, 2023

CFA Exam: Sharpe Ratio, Sortino Ratio, Calmar Ratio, MAR Ratio

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The performance of alternative investments can be evaluated by analyzing the distribution of returns on investment. Traditional methods involve using statistical parameters such as variance or standard deviation. Note that these measures are not suitable for assessing the risk involved in alternative investments.

This is because alternative investment returns don't have a normal distribution and are characterized by asymmetry and extreme observations. This kind of anomalous or non-standard distribution requires some additional parameters, which include skewness and kurtosis.

Skewness is used for identifying distribution asymmetry and kurtosis is a measure of the concentration and the peakedness of a distribution. The distribution of alternative investment returns is most commonly characterized by negative skewness and high kurtosis.

Sharpe Ratio

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Sharpe Ratio
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\(S=\frac{{R}_P - {R}_F}{\sigma_P}\)

  • S - Sharpe ratio
  • \({R}_P\) - return on a portfolio
  • \({R}_F\) - return on the risk free asset
  • \(\sigma_P\) - standard deviation of return on a portfolio
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Because the distribution of rates of return for alternative investments is rarely normal and generally isn’t symmetrical and the liquidity of alternative investments is low, using the Sharpe ratio to evaluate investment may be inappropriate.

Sortino Ratio

To assess the risk of alternative investment, it’s better to use measures that show the risk of loss, namely downside risk measures.

These include value at risk or safety-first risk measures or the Sortino ratio. Since all these measures use standard deviation and are calculated assuming a normal distribution, you should remember that they underestimate the risk for negatively skewed distributions.

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Sortino Ratio
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\(S_T=\frac{{R}_P - {R}_F}{\sigma_D}\)

  • \(S_T\) - Sortino ratio
  • \({R}_P\) - return on a portfolio
  • \({R}_F\) - return on the risk free asset
  • \(\sigma_D\) - downside deviation of the portfolio
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For the Sortino ratio, the numerator is exactly the same as in the case of the Sharpe ratio, but the denominator includes the downside deviation of the portfolio. As a result, we get a risk measure that is better suited for high-volatility portfolios.

Calmar Ratio & MAR Ratio

The alternatives to the ratios mentioned above include the 2 following ratios:

  • MAR ratio, and
  • Calmar ratio.

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CFA Exam: IRR, MOIC & Cap Rate

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For different investments, different measures of portfolio performance should be used. For example, private equity returns but very often also real estate returns are described by the so-called J-curve effect.

In these types of investments, money is spent for a longer period of time (several years in the case of private equity) and positive cash flows begin to appear in the following years after the fund exits its investments. Hence the net cash flow curve resembles a hockey stick and that’s why it’s called the J-curve.

We have negative cash flows at the beginning and as time passes by the positive cash flows start to appear.

Internal Rate of Return (IRR)

If we assume that a fund manager decides about the choice of investments and timing, the single best measure to evaluate the performance of the fund manager would be the IRR (aka. money-weighted return).

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Internal Rate of Return (Money-Weighted Return)
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\(\Sigma^{n}_{t=0}\frac{CF_{t}}{(1+IRR)^{t}}=0\)

  • \(CF_{t}\) - after-tax cash flow at time "t"
  • \(IRR\) - internal rate of return
  • \(t\) - moment of time
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The IRR takes into account the timing and value of cash inflows and outflows. Of course, the IRR has its disadvantages, e.g., in its basic formula, it assumes that positive cash flows will be reinvested using the same IRR rate, which is rarely the case in reality.

Multiple on Invested Capital (MOIC)

Also other measures – that are easier to interpret – can be used with private equity and real estate investments. One such measure is the multiple on invested capital (MOIC) or simply money multiple.

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Multiple on Invested Capital (MOIC)
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\(MOIC=\frac{i_r+i_u}{c}\)

  • \(r_i\) - realized value of investments
  • \(r_u\) - unrealized value of investments
  • \(c\) - total amount of invested capital

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Cap Rate

In the case of real estate investments, we also very often use the so-called cap rate to evaluate the performance of the investment. Cap rate is a fairly simple measure given by the following formula that you can use in your level 1 CFA exam:

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Cap Rate
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\(r_c=\frac{NOI}{V}\)

  • \(r_c\) - cap rate
  • \(NOI\) - net operating income
  • \(V\) - market value of property
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Level 1 CFA Exam Takeaways: Performance Appraisal

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  1. The performance of alternative investments can be evaluated by analyzing the distribution of returns on investment.
  2. For the Sortino ratio, the numerator is exactly the same as in the case of the Sharpe ratio, but the denominator includes the downside deviation of the portfolio.
  3. A maximum drawdown is the difference between the maximum and minimum value of a portfolio in a period of time, measured in percentage points.
  4. The difference between the MAR ratio and Calmar ratio is the period of time for which we take the value of return and maximum drawdown. For the former, it is the time from fund inception until today and for the latter – some predefined period of time, usually 36 months.
  5. Private equity returns but very often also real estate returns are described by the so-called J-curve effect.
  6. Money multiple is easy to interpret. If e.g. it’s equal to 3.5x it means that the total return is 3.5 times bigger than the invested capital.
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