CFA Level II 2017 Mock Exam PM - Q38 Arbitrage Free Conditions

Hi, could someone help explain Q38 on Arbitrage-Free conditions on the recent CFA Level II 2017 Mock Exam PM?

Why is Condition 1 incorrect? Isn’t a higher risk security also mean a higher expected return? Also, how is Condition 3 correct? How does the price of the portfolio equal the sum of individual securities?

The answer suggests that the principle of no-arb only applies to risk-free and not risky securities? What does it even mean?

Sorry for the questions - hope to get clarifications if possible

condition 3 is the “dominance” principle.

suppose you have a 2 year 5% coupon bond with 100 par value. this is equal to having a 2 zero-coupon bonds, 1 paying 5 bucks at the first year and one paying 105 bucks at the end of the 2nd year. under the arbitrage-free conditions, these two forms of holdings should be priced equally (the 2 year 5% bond and the 2 zero coupon bonds each with a face value of 5 and 105), this is what they mean by sum of individual securities.

I approached this question simply by eliminating condition 2 and 3 which are both correct.

ok thanks Edbert! you’ve been super helpful

so if I’m understanding correctly, the “dominance” principle is essentially the unbiased expectations theory where you are risk neutral between bonds of different maturity but with same cash-flow profile

in a way it’s saying that cash flows (including discounts) are additive if I’m understanding this correctly

no, it’s not unbiased expectations theory (actually, let me revise those bloody theories and will come back to you later). it’s about pricing bonds using spot rates or using ytm resulting in the same price (remember level 1 where we priced bonds using spot rates and ytm?).

if A + B = 2

and A is 1, therefore B must be 1, otherwise there’s going to be an arbitrage.