Final answer:
The annualized holding period return is calculated by taking the total cash flow from the bond (interest payments minus capital loss) over the holding period, dividing it by the purchase price, and then adjusting for the number of years held. For the bond purchase and sell example, the annualized return would be calculated with an incurred loss due to the sale at a price lower than the purchase price.
Step-by-step explanation:
You asked how to calculate the annualized holding period return if you purchased a bond 3 years ago, which had a 14-year maturity and a 2.7% annual coupon, at $104 per $100 of face value, and sold it today at $93 per $100 of face value after yields rose to 4.71%. To answer this, we need to consider both the capital gains or losses and interest payments of the bond over the holding period. We also need to adjust our calculation to an annualized basis since the holding period is not one year.
The coupon received annually is 2.7% of the face value ($100), which amounts to $2.70 per bond. Over three years, you have received a total of 3 * $2.70 = $8.10 in interest payments. You bought the bond for $104 and sold it for $93, incurring a capital loss of $11. Hence, the total cash flow from this investment is the sum of interest received minus the capital loss: $8.10 - $11 = -$2.90 per $100 of face value.
The formula to calculate the holding period return (HPR) is: (Ending Value - Beginning Value + Income) / Beginning Value. To annualize this return, we raise it to the power of (1/number of years) and subtract 1. So, the approximate annualized HPR is: ((-2.90 + 104) / 104)^(1/3) - 1. Please note the calculation would be slightly different with the actual bond's face value and the exact cash flows over the period.
Remember, the annualized holding period return considers both the income received from coupon payments and the capital gain or loss from the sale of the bond compared to its purchase price, adjusted on an annual basis.