Please show work no excel Suppose you observe the following for today\'s term st
ID: 2811826 • Letter: P
Question
Please show work no excel
Suppose you observe the following for today's term structure for risk-free securities: Effective Annual YTM 1-year zero-coupon bond 3.6% 2-year zero-coupon bond 3.4% 3-year zero-coupon bond 3.2%
a. Suppose you believe that the term structure next year will be the same as today's term structure. If today you buy the 3-year zero coupon bond, what do you expect your holding period return will be between now and one year from today?
b. What should be today's yield to maturity on a 3-year, 8% annual coupon risk-free bond? (Express as accurate as 1.234%)
Explanation / Answer
a)
yield on a 3-year zero-coupon bond , y = 3.2% = 0.032
assuming maturity value of zero coupon bond , m = $1000
price of 3-year zero coupon bond today, p= m/((1+y)3) = 1000/((1.032)3) = $909.83137
yield on 2 -year zero coupon bond , y1 = 3.4% = 0.034
price of 3-year zero coupon bond 1 year from now, p1 = m/((1+y1)2 ) = 1000/(1.034)2 = $935.31720
expected holding period return = (p1-p)/p = (935.31720-909.83137)/909.83137 = 0.028012 or 2.8012% or 2.80%
b)
let the yield on 1 year zero coupon bond = y0 = 3.6% = 0.036
annual coupon rate , c = 8% = 0.08
annual coupon value , C = c*m = 0.08*1000 = $80
price of bond, p = [C/(1+y0) ] + [C/(1+y1)2 ] + [(C+m)/(1+y)3 ]
p = [80/(1.036) ] + [80/(1.034)2 ] + [(1080)/(1.032)3 ]
p = 77.220077 + 74.825376 + 982.617882 = 1134.663335 or 1134.66
let ytm of coupon bond = x
p = [C/(1+x) ] + [C/(1+x)2 ] + [(C+m)/(1+x)3 ]
1134.66 = [80/(1+x) ] + [80/(1+x)2 ] + [(1080)/(1+x)3 ]
by trial and error we will find that , x = 0.032192 or 3.2192% or 3.22% ( after rounding off to 2 decimal places)
ytm = 0.032192 or 3.2192% or 3.22% ( after rounding off to 2 decimal places)