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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

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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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  • $\begingroup$ Thank you for your fast response. If I would use historical data how do I account for the time left to expiry? The risk on a fresh 30y bond is different than the risk on a 30y bond that has been alive for 20y already. Would I collect a time series of strictly freshly issued 30y bonds and then compute the 1-year Holding Period return (HPR) for each of the bonds? $\endgroup$ – mbison Dec 28 '17 at 8:35
  • $\begingroup$ You should ideally construct time series that closely mirror the way you invest. By convention, bond indices are rebalanced monthly. For example, the 30-year benchmark index is assumed to buy the most recently issued 30-year bond at the end of a month, and hold that same bond for the next month. At the end of the next month, if another 30-year benchmark has been issued, the index rule assumes that you sell the old one and buy the new one. $\endgroup$ – Helin Dec 28 '17 at 17:54

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