The formula for computing forward price is S * (1+R)^T

T = forward contract term in years

R = annual risk-free rate

S = spot

Q1. 3m forward contract on zero coupn bond. Spot - 500, annual risk free R = 6%. Calculate forward price

In book, the answer = 500 * (1.06)^.25 = 507.34 ---- here, R & T are in annual terms

My method was the most basic. I converted rate into months, and so T. So, my answer = FP = 500 * (1.005) ^ 3 = 507.54 - minor difference of 0.20. Is this also right? As we have been doing since birth.

Q2. 100-day forward on a stock, Spot = 30, expected dividend = 0.40 in 15 days, and 0.40 in 85 days. R = 5%, and yield curve is flat.

What is the significance of “yield curve is flat”?

Now, According to book, PVD (present vale of dividend) = 0.40 / 1.05 ^ 15/365 + 0.40 / 1.05 ^ 85/365 = 0.7946

Q1: You’re treating the risk-free rate as if it were a nominal rate, compounded monthly; they’re treating it as an effective rate.

Even if it were a nominal rate, it wouldn’t be compounded monthly; it would be compounded quarterly (as it’s being quoted for a 3-month bond.

Unless they tell you that the rate is nominal – that it’s BEY, or LIBOR, or an annual rate for a monthly-pay mortgage – you should assume that it’s an effective rate.

Q2: Same thing: you’re assuming that the rate is a nominal rate, not an effective rate.

The significance of the yield curve being flat is that you apply the same rate to dividends received at different times; if the yield curve weren’t flat you would likely have different spot rates for each dividend.

Gotcha! Now, guess I’ll have to decode the effective vs nominal. The basic I know that nominal means 6% pa compounded semi-annually, while effective is (1.03)^2 - 1 = 6.09%. But I have a mental block understanding the rate put this way here. Let me pedal my brainometer harder.