AppliedNumeric answerFree solution

An index is at 4,0004{,}000, rates are 5%5\% and the dividend yield is 2%2\%, both continuously compounded. What is the six-month forward, to the nearest point?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

4,0604{,}060

A forward is spot carried to delivery, and the carry here is financing minus the dividends you forgo: F0=S0e(r−q)T=4000 e(0.05−0.02)(0.5)=4000×1.01511≈4,060F_0 = S_0 e^{(r-q)T} = 4000\,e^{(0.05-0.02)(0.5)} = 4000 \times 1.01511 \approx 4{,}060. The arithmetic shortcut is that net carry is 3%3\% a year, so half a year is about 1.5%1.5\% of 4,0004{,}000, which is 6060 points. Nothing about anyone’s forecast enters: cash and carry enforces the level, since a forward away from it is a riskless trade against the spot market.

Worked solution

  1. Formula
    F0=S0e(r−q)TF_0 = S_0 e^{(r-q)T}
  2. Substitute
    =4000 e(0.05−0.02)(0.5)= 4000\, e^{(0.05-0.02)(0.5)}
  3. Solve
    =4000×1.01511= 4000 \times 1.01511
  4. Answer
    F0≈4,060F_0 \approx 4{,}060

Sanity check. Above spot because financing costs more than the dividends pay.

Takeaway: A forward is spot plus carry, enforced by cash and carry – not a forecast.

Answer it in practice – your answer is marked and recorded.

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