Overvalued Bond

CFA Level II Fixed Income
#1

[question removed by moderator]

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

#2

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

#3

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.

#4

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

#5

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

#6

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”