Question

(a)        You are given the spot rates  s₅ = 3%  and  s₁₀ = 5% .  

If these are the only spot rates that you know, would you say that the yield curve is normal, flat, or inverted?  Explain.

(Note:  A correct answer without a correct explanation earns no credit.)

(b)       With the information in part (a), calculate the forward rate ₅ f₅ .

(c)        Assume a perfectly flat yield curve, i.e., s_t is the same constant value, say c , for all t.  Show mathematically that the forward rate _mf _t is the same constant c for all m and t.

Answer 1

a) spot rates  s₅ = 3%  and  s₁₀ = 5% .

So we can see that there is an increase in spot rate i.e.., by 2 % so the graph will be increasing which means normal

b)

c)

So the value given is c

from the above graph we have for all values of t,m

putting in above equation

The forward rate _mf _t is the same constant c for all m and t.