Calculating a Bond Sharpe Ratio from Total Returns
Summary
The note answers how to calculate a Sharpe ratio for a bond by treating it as a return-producing asset, just like a stock. Rather than combining yield to maturity with duration-scaled yield volatility, it recommends constructing a time series of total returns over holding periods and applying the usual performance calculation to that series. Total return should account for both price changes and income from coupon payments.
For broad bond markets, the answer points to daily total-return indices from major index providers as an available input. For individual bonds, a suitable index may be unavailable, so the investor may need to build a total-return series from bond prices and interest payments. The response does not specify the risk-free rate convention, return frequency, annualization method, or treatment of changing bond characteristics. Those choices must be made consistently for a meaningful Sharpe comparison.
Key ideas
- Bond performance metrics can be calculated from a time series of holding-period total returns.
- Bond total returns include both price changes and coupon income.
- Yield to maturity and duration-scaled yield volatility are not presented as substitutes for realized total-return data.
- Market-segment indices may provide daily total returns, while an individual bond series may need to be constructed.
- Return frequency and Sharpe calculation conventions should be aligned, though the answer does not prescribe them.
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Full text
# how is the sharpe ratio (or other risk/return measure) computed for a bond? # how is the sharpe ratio (or other risk/return measure) computed for a bond? What is the industry norm to compute a sharpe ratio for a bond? For a stock one would typically take a time series of daily returns, compute the average daily return, compute the standard deviation of the daily returns and use this to compute the Sharpe. In the absence of credit risk, how does one go about this problem for a bond? Assume we hold a T period Bond, with a coupon of C. I was thinking of the following, but wasn't sure if correct. - For the risk (denumerator): duration * stdev(T-yr yield)? - For the reward (numerator): ytm? Or should one use historical average of holding-period-returns for the reward? and also historical stdev of holdingperiod returns (multiplied with duration) for the risk? Thanks ## Answer by Helin (score 0, accepted) https://quant.stackexchange.com/a/37517 It's identical to a stock. For any asset (bonds included), you can calculate a time series of total returns of holding the asset over time, which can then be used to compute any performance metrics (Sharpe ratio included). For broader market segments (e.g., US Treasuries, US investment grade corporates, global sovereigns, etc.), total return indices are computed daily by various index providers, including Bloomberg (formerly Barclays and formerly Lehman), Russell (formerly Citi), and ICE (formerly Merrill Lynch). As to individual bonds, some of the index providers also provide indices (at least for rolling benchmark Treasuries). But most of the time, you'd probably need to compute a total return index yourself (which is identical to how you'd compute a total return index for a stock – but using prices and interest payments, as opposed to prices and dividends).
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