CFAI 2016 AM (Fixed Income - Scott)

[blackscholesvol]

I don’t quite understand this question. The answer indicates that the bond is overvalued vs. its intrinsic value. They indicate that if an investor purchases a US Treasury bond at $101.5 and holds the bond for two years, at which time the 1 year, 2, year, and 3 year spot rates are all 8%.
Just looking at the initial forward curve indicates that the forwards in 2 years would be 7.03%, 9.06%, and 11.1% which are mostly HIGHER. Since they expect spot rates to rise lower than expected, shouldn’t the bond be under-valued.
Year Spot Forward
1 3%
2 4% 4.01%
3 5% 7.03%
4 6% 9.06%
5 7% 11.1%

 

[thtsejacgmail.com]

Agree.. and I have no idea how the heck do they get 1.86% total return. I got IRR of 4.93-4.94%.
Hoping someone could shed light on this horrible question

 

[parth_993]

Even i had marked undervalued and got it wrong. S2000 ?

 

[blackscholesvol]

Soneone has got to know this? Anyoneeeee?

 

[stevoDE]

The cash flows are discounted back at the relevant spot rates. 8% is greater than all of the current spot rates and will produce a lower present value therefore the bond is currently overvalued relative to the bond price using spot rates of 8%.

 

[blackscholesvol]

The 8% is the expected future spot rate. A one year spot rate in 3 Years is 8%. A two year spot rate in 3 years is 8% and a three year spot rate in 3 years is 8%.
It should be compared with the forward curves…..something’s not right

 

[inchvbeam]

Anyone can help on getting the-1.86% return for the 2 years please? Thanks.

 

[Batman1]

You need to compare to the spot curve

 

[inchvbeam]

Sorry i dont understand - anyone could further explain this please? thanks.

 

[0cean27]

The answer compares the future one year spot rate (8%) to 2f1 (7.03%). However since this is a 5 year bond, and after 2 years there are still 3 years left until maturity, I think what we should be comparing is the future expected 3 year spot rate (still 8%) and 2f3 implied by current spot curve (9.04%, which is derived from this equation (1+4%)^2 . (1+2f3)^3 = (1+7%)^5). So yeah, I think it should be undervalued.

 

[data storm]

I agree with you. it seems that there’s something here as i should use the forward rates which will yeild a price that’s lower than the expected spot

 

[achokshi]

I interpreted this question based on the original pricing. The original pricing of the bond was 101.5 based on the spot & forward curve. Since the expected future spot rates (8%) is greater than the actual forward rate for 3 years, the bond has been mispriced based on the forward rate being lower than the expected future spot rate (which leads it to be overvalued).
In other words, the price of the bond would fall greater than expected based on the forward rate curve, and therefore is overpriced.

 

[h21]

achokshi wrote:
I interpreted this question based on the original pricing. The original pricing of the bond was 101.5 based on the spot & forward curve. Since the expected future spot rates (8%) is greater than the actual forward rate for 3 years, the bond has been mispriced based on the forward rate being lower than the expected future spot rate (which leads it to be overvalued).
In other words, the price of the bond would fall greater than expected based on the forward rate curve, and therefore is overpriced.

I get your idea, while I get the spot rate, so you are saying in future, we were expecting to discount the cash flow after year two with the lower forward rate, which would get a higher price than the expected spot rate price, thus over value?

 

[inchvbeam]

sorry, then how does the -1.86% provided in the answers comes into play?