Question

Given the following actual return information, if the mean is 0.057 then what is the variance of the returns for SpaceX?

Year    Actual Return

1.        0.256
2.        0.069
3.       -0.154

If Pro Bass Shop’s twenty-year bonds are currently selling for $992, the coupon rate is 4.6% and coupons are semi-annual, then what is the YTM?

Answer 1

a.

Variance = [{ (Rerurn1 - Mean)^2+(Rerurn2 - Mean)^2+(Rerurn3 - Mean)^2 }/(Sample size -1) ]

Variance = { (0.256 -0.057)^2 + (0.069 - 0.057)^2 + (-0.154 - 0.057)^2 }/(3-1)

= 0.042133 Answer

b.

We know that,

Price of the bond = Present value of semi annual coupon and face value discounted at semi annual ytm.

Face Value = 1000

Semi annual coupon = 4.6% * 1000/2 = 23

Number of payments = 20*2 = 40

Semi annual ytm = ?

992 = 23/(1+semi annual ytm)^1 + 23/(1+semi annual ytm)^2 + 23/(1+semi annual ytm)^3 + 23/(1+semi annual ytm)^4 + 23/(1+semi annual ytm)^5 + 23/(1+semi annual ytm)^6 + 23/(1+semi annual ytm)^7 + 23/(1+semi annual ytm)^8 +............. 23/(1+semi annual ytm)^40 + 1000/(1+semi annual ytm)^40

We will use heat and trial method to get that value for which above equation satisfy.

Semi annual ytm = 2.33%

YTM = 4.66% Answer