Free SOA Exam FM (Financial Mathematics) Bonds Practice Questions

A callable bond gives the issuer (not the bondholder) the right to redeem the bond before its stated maturity date, typically at a specified call price.

Choice A is incorrect because it describes a putable bond, where the bondholder (not the issuer) has the right to sell back.
Choice C is incorrect because the ability to purchase at par is unrelated to callability.
Choice D is incorrect because adjustable coupon payments describe a floating rate feature, not callability.
Choice E is incorrect because trading restrictions relate to tradability, not the call feature.

For a premium bond ($P > C$), we have $Fr > Cj$. The book value starts above $C$ and decreases each period toward $C$.

The amortization of premium in period $t$ is $PA_t = Fr - j \cdot B_{t-1}$. Since $B_{t-1}$ decreases over time, $j \cdot B_{t-1}$ decreases, making $PA_t$ larger. So the amortization of premium increases each period.

(A) is correct: book value decreases and amortization amounts increase.

(B) is wrong — book value decreases for premium bonds, not increases. (C) is wrong — for premium bonds, the coupon exceeds interest earned. (D) is wrong — the amortization amounts change each period. (E) is wrong — interest earned decreases (not increases) because book value decreases.

Accumulated value at maturity:
$AV = 60 \cdot s_{\overline{20}|0.04} + 1{,}000$.

$s_{\overline{20}|0.04} = \frac{(1.04)^{20} - 1}{0.04} = \frac{2.191123 - 1}{0.04} = 29.778079$.

$AV = 60(29.778079) + 1{,}000 = 1{,}786.68 + 1{,}000 = 2{,}786.68$.

Realized yield: $j = (AV/P)^{1/n} - 1 = (2{,}786.68/1{,}000)^{1/20} - 1$.

$\ln(2.78668) = 1.02482$. $1.02482/20 = 0.05124$. $e^{0.05124} = 1.05257$.

$j \approx 5.26\%$.

The realized yield is between the coupon rate (6%) and reinvestment rate (4%), closer to the geometric mean.

(B) $6\%$ requires reinvestment at 6%. (C) $4\%$ is only the reinvestment rate. (D) and (A) don't match the calculation.