In: Finance
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%. (
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%