Question

How do you calculate the average return of a bond per week/month?

How do we also get the sharpe ratio once the average return in calculated.

Answer 1

Return is basically the profit earned over the principal invested. For bonds, the return is given by the bond yield which is the ratio of Interest earned and the Bond price. For this we need, Bond face value, its years to maturity, annual coupon rate, and the frequency of coupon payment and the yield to maturity (YTM). Using these data, we can calculate the present value of bond using the below formula:

Suppose FV is the face value of the bond.  CF is the annual coupon payment n is the maturity of the bond and r is the YTM. So, the present value of the bond is given by the below formula.

Bond yield = Interest earned / present value of the bond

The bond yield can be converted into weekly/ monthly Yield. Average monthly return can be calculated by taking the average of all the monthly returns.

From the above calculation of return, we can calculate the Sharpe ratio using the formula below:

Sharpe ratio = (R_p - R_f) / σ_p

R_p - Return on portfolio

R_f - Rish free rate

σ_p - Standard deviation of portfolio

Standard Deviation is calculated using the formula:

where, μ is the average return, X are the returns and n is the sample size. Hence we can calculate the Sharpe ratio - Sharpe ratio = (R_p - R_f) / σ_p