Fixed Income - Challenge Questions - Need Intuition

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mattkendrick

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[question removed by moderator]
Answer is A, but how? I don’t understand!

[question removed by moderator]
Answer is B…how?! My mind is broken. I would appreciate some help on these questions! Please and thanks!
 
1) 1-0.0475/4 = 1/[(1 + bey/2)^0.5] solve for BEY which should be 4.87%
Edit: I originally put in 0.475/4.
 
Thanks breadmaker, I think I understand question 1, we need to find the P0 first right? Using this formula: i = Pf - P0 / Pf x 360/t
Since commerical paper has a price of 100, it’s 0.0475 = 100-P0 / 100 x 360/90, then we get P0 of: 98.81
Then: we input P0 into: BEY = (Pf - P0) / P0 x 365/t
= (100-98.81) / 98.81 x 365/90
=4.88% rounding i guess…
What about question 2?
 
In order to compute the present value of the bond, you need to discount each of its payments with the appropriate spot rate. For instance, the first payment is in 6months, thus you need the 6 month spot rate (which is not provided here). For the second payment in 1 year, you need the 1 year spot rate (also not provided). Spot rates can be calculated from the forward rates:
An example, the 1.5 year spot rate can be calculated as:
S1.5Y= S6m * F6m1y
where S stands for spot rate and F for forward rate. 6m1y means, the rate in 6months for 1 year.
If you have the S1.5Y, you could use that in order to discount the bond payment you are receiving in 1.5 years. Same for the other ones.
Let me know if this is not cear.
 
2.5/(1.006) + 2.5/(1.006*1.009) + 2.5/(1.006*1.009*1.0115) + 2.5/(1.006*1.009*1.0115*1.0135) + 102.5/(1.006*1.009*1.0115*1.0135*1.015) = 106.83
use the forward rates divided by 2
 
I think I get it, thanks tartaglia and bin_english. However, I am wondering how we figure out 102.5 for the last part? It’s a bit confusing as there is a 5% coupon rate, but we didn’t use it on our calculation? I might be mistaken. The only way I see a pattern is 100 par value plus 2.5 years, but that makes no sense.
 
Coupon Payments are typically made semi-annualy, but are quoted on an annual basis, so you divide the coupon by 2. In the final year, investor receives the entire Face Value back, thus you have coupon payment plus the face value (typically 100), 102.5.
 
I think there is something wrong with the question however.
I agree with bin_english’s approach, however, that requires that the forwards are each for 6 months (the 6 month rate 1 period from now, the 6 month rate 1 year from now etc.). However, that table makes it sound like the forwards are for longer periods. Maybe double if you copied it correctly, or if they made a mistake there.
 
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