CFAI Reading 23 P.111 Q # 3B

They ask you to calculate the expected total risk premium of the 3 securities in the exhibit and determine the investor’s probably course of action. Here’s the data they include in the exhibit: Real Risk Free Int. Rate = 1.2% Current Inflation = 2.2% Spread of a 10-Year Over 1-Year Treasury Note = 1.0% Long-Term Inflation Expectation = 2.6% 10-Year MBS Pre-Payment Risk Spread Over 10-Year Note = 95bps 10-Year Call Risk Spread = 80bps 10-Year BBB Credit Risk Spread Over 10-Year Note = 90bps The 3 securities in question are: #1. 1-Year U.S Treasury Note #2. 10-Year BBB/BAA Rated Corporate Bond (Callable) #3. 10-Year MBS (Callable, Gov’t Backed Collateral) From what I can remember, Risk Premium Approach: Rf + (TIMID) or Rf + Tax Premium + Inflation Premium + Maturity Premium + Illiquidity Premium + Default Premium So the have the Expected Total Risk Premium calculated as follows: [0% + (1.0% + 0.8% + 0.9%) + 0.95%] / 3 = 1.22% - 1.00% = 0.22% My question is twofold: #1. Why did they include the 1% spread over 10-year t-bonds for the calculation of the callable bond (presumably the middle portion of the calculation above indicated as (1 + 0.8 + 0.9) and not for the MBS which they just used 0.95%? #2. Why did they subtract 1%? Was really hoping someone could shed some light on this entire #3 problem as I can envision something like this being on the exam and can easily trick us with simple omissions etc… THanks

#1: the 0.95% already includes both a premium for prepayment and a maturity premium for a 10yr tenor, check the small text behind the table #2: the only explanation I see is that you must see spread OVER THE SIMILAR TREASURY BOND: + The similar treasury bond is a 10 year treasury bond, which already includes a 1% maturity premium (10yr Vs 1yr) + So, from average premium of your basket of 3 bonds, you “take out” the 1% that compensates for maturity premium, in order to capture the “pure” premium above the 10yr treasury bond + Is like, once you get the average exp return of 5.02%, substracting the T-Bond ex preturn (4.8% = 1.2% + 2.6% + 1%) = 0.22% Even though, there is one problem, which makes this problem misleading: they are substracting the 1% (because of the 10yr maturity) to the average, which includes a 1yr note… in that case the 10 yr would not be “the similar treasury bond”, at least that is my opinion. Instead: + 1y T note = 1.2% + 2.6% = 3.8% + Similar T bond = itself, so spread above similar T bond = 0% + 10y Corp bond = 1.2% + 2.6% + 1% + 0.8% + 0.9% = 6.5% + Similar T bond = 10y T bond = 1.2% + 2.6% + 1% = 4.8% + Spread above similar t bond = 6.5% - 4.8% = 1.7% + 10y MBS = 1.2% + 2.6% + 0.95% = 4.75% + Similar T bond = 10y T bond = 1.2% + 2.6% + 1% = 4.8% + Spread above similar t bond = 4.75% - 4.8% = -0.05% Average spread above similar t bond = (0% + 1.7% -0.05%) / 3 = 0.55% So you would actually buy it… The difference is assume that the 10yr Treasury Bond is the similar one “for the whole package”… Again, this is only my opinion. I guess in the exam we will not face something with such a confusing wording. Hope it helps

regardless of my opinion about the suitability of a 10 year T-Bond as “the similar” to a 1 year T-Note for comparisons, I have serious doubts that a 10 year Mortgage Backed Security offers less compensation than a 10 year Treasury Bond, as it is in this example… Really, if you know the “Rf + TIMID”, forget about this particular example of cfa text. It is going to confuse you with something that I guess you in fact know

There was an errata on this, they changed it from “similar-term treasury” to “10-year treasury bond”