1. Over the next year, what is the current yield, capital gains yield, and total return...

1. Over the next year, what is the current yield, capital gains yield, and total return (or total yield) of a 5 year bond with a 4% YTM and a coupon rate of 5%? Assume the YTM over the next year remains the same.

2. Same question as above, except the YTM at the end of the year has risen to 4.5%. (

Solutions

Expert Solution

Q1. Total Return = Current Yield + Capital Gains Yield

Current Yield = Annual Coupon/Current Price of the bond

Capital Gains Yield = (Price of bond 1 yr later - Price of bond today)/Price of bond today

We need to calculate price of bond today and 1 yr later.

where P is price of a bond with Annual coupon C, YTM i, M face value and n periods to maturity

Assume M = 100, C = 5% * $100 = $5, n=5, i = 4%

Price of bond today = 22.2591 + 82.1927 = 104.45

Price of bond 1 year later:

Price of bond 1 Yr later = 18.1495 + 85.4804 = 103.63

Current Yield = 5/104.45 = 4.79%

Capital gains yield = (103.63 - 104.45)/104.45 = -0.785%

Total Yield = 4.79% - 0.785% = 4.0049%

Question 2

Now, the YTM here rises to 4.5% as the end of year. So the price of bond after year 1:

Price of bond 1 Yr later = 17.9376 + 83.8561 = 101.79

Current Yield = 5/104.45 = 4.79%

Capital gains yield = (101.79 - 104.45)/104.45 = -2.55%

Total Yield = 4.79% - 2.55% = 2.2433%

jeff jeffy answered 1 year ago

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