Calculating Sharpe Ratios for Equal-Volatility Stock Portfolios

Summary

The document raises questions about constructing an equal-volatility portfolio from daily stock returns and measuring its Sharpe ratio. The investor describes calculating log returns, scaling each stock’s returns using a rolling volatility estimate, and averaging the scaled series. They ask whether that average represents portfolio returns when assets are allocated on an equal-volatility basis, and whether annualizing its mean-to-standard-deviation ratio produces a meaningful Sharpe ratio.

The reported Sharpe estimate is implausibly high to the author, prompting questions about how such a figure compares with published performance measures and whether it can be translated into realized returns. The document does not include an answer or resolve the calculation. In particular, it leaves open how the volatility scaling maps to actual portfolio weights, and how rebalancing, return aggregation, risk-free returns, and the use of rolling estimates affect the result.

Key ideas

• The author proposes scaling stock returns by rolling volatility and averaging them to represent an equal-volatility portfolio.
• The author asks whether this return series supports a standard annualized Sharpe calculation.
• The reported Sharpe estimate prompts a question about whether the portfolio construction or calculation is flawed.
• The document provides no answer, so the weighting and Sharpe methodology remain unresolved.

Tags

# How do I calculate the sharpe ratio of a portfolio of stocks?


# How do I calculate the sharpe ratio of a portfolio of stocks?












If I have daily prices for $N$ stocks, how do I calculate the Sharpe ratio for an equal volatility weight portfolio?

On each day, I have calculated log returns as: $$ r_{t}^{s} = \ln{price_{t}\over{price_{t-1}}} $$

I have then measured the standard deviation of each this series in a 60-day window, and normalised this so each series has approximate deviation of 1.

Question 1:

Is the portfolio daily return equal to the arithmetic mean of the individual stocks $s$, assuming I will allocate on a equal volatility basis before trading:

$$ \text{Portfolio Log Return}_t = \frac{1}{N} \sum_s r_t^s $$

Question 2:

If I take the portfolio return from above, and use these figures to create a Sharpe ratio

$$ \text{Sharpe ratio} = \frac{\sqrt(252)*\text{Arithmetic Average of LogReturns}}{\text{Std Deviation of LogReturns}} $$

- Does this make any sense?

- What's the relationship of a Sharpe ratio calculated in this way to the Sharpe ratios published in journals and fund brochures?

- Can a Sharpe calculated in this way be converted back to 'realized returns'?

I have calculated this value for a period 1993-1997 for the 500 most traded stocks, weighted an equal volatility basis, and got a value of approximately 7, which is definitely not right.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.