Computation of forward / spot price

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

My method - 0.40 / (1 + 5% * 15/365) + 0.40 / (1 + 5% * 85/365) = 0.7984

A variation of .0038… Which method to use?

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.

It means that when it’s BEY (compounded semiannually), but not necessaarily in general. You have to know how often it’s compounded.

This article I wrote may help: