Question

You own a S1,000 face value, zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year and believe that the required yield next year will have the following probability distribution: Probability 0.1 Required Yield 5.50% 5.75% 0.1 0.6 6.00% 625°/o 0.1 0.1 6.50% a. What is your expected price when you sell the bond? b. What is the standard deviation?

Answer 1

	Probability [p]	Required Yield [r]	Bond price 1 year from now [v]	E[v] = v*p	d = v-E[v]	d^2	p*d^2
	0.1	5.50	$         807.22	$       80.72	$     15.08	$    227.31	$        22.73
	0.1	5.75	$         799.61	$       79.96	$        7.47	$       55.81	$           5.58
	0.6	6.00	$         792.09	$     475.26	$      -0.05	$         0.00	$           0.00
	0.1	6.25	$         784.66	$       78.47	$      -7.48	$       55.88	$           5.59
	0.1	6.50	$         777.32	$       77.73	$    -14.82	$    219.54	$        21.95
	Note:			$     792.14			$        55.85
	Bond price 1 year later for 5.50% yield = 1/1.055^4 =				$        0.81
a)	Expected price when the bond is sold = $792.14.
b)	Standard deviation = 55.85^0.5 = $7.47