Overvalued Bond

[question removed by moderator]

Can anyone explain why the bond is overvalued if the expected spot rate is higher than current forward rate

because, it is discounted using the “higher expected” spot rate at each cash flow date. yeilding a lower value compared to the current one.

Imagine you have to discount $100. The market discounts it at 5% so the PV=100/1.05=95.24

You believe the discount should be 10% so the PV should be 100/1.1=90.91. So you say the market is overvaluing the bond.

Expected spot rate = what the market actually is, when it happens

Forward rate = what was PERCEIVED to be the rate.


Step 1: Overvaluation = Perceived price > THE ACTUAL price,

Step 2: Perceived yield < Actual yield

Forward rate = perceived yield Expected spot rate = Actual yield at ‘expected’ point of time

Nice points, I also used to mix this up… its clearer now.

It confuses me. Could you please confirm what I write here is correct or not

  • Suppose you have a price a (x+y)-maturity bond, which is calculated by this formula

P_real = (1+R(0,x))^(-x) * (1+R(x,y))^(-y) given the spot rate R(0,x) and the forward rate R(x,y)

( R(x,y) means y-year forward rate x-year from now)

  • You think that the R(x,y) must be higher, and you call this value S(x,y) - expected spot rate

  • The price of bond is so expected as P_expected = (1+R(0,x))^(-x) * (1+S(x,y))^(-y)

  • Because S(x,y) > R(x,y) , the P_expected is lower than the P_real. So, we say the bond is overvalued.

My only concern is that I don’t know why they call the “expected forward rate” “expected spot rate”