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Unformatted text preview: s than the expected payoﬀ of .3/1.025?
Answer: Less. Example (continued)
Why should it be worth less then its expected discounted value?
This security is very correlated with the market
High β ⇒ high expected return according to CAPM. It pays you money exactly when you least need it.
So it costs less than .3/(1 + r ). Say that it costs .26/(1 + r ).
.26 reﬂects the risk-neutral probability
The average return is:
.3 − 1.26
E [payoﬀ] − price
If the price was .3, then the expected return would be 2.5% or just
the riskless-rate. Connecting Risk-Neutral and Actual Probabilities Notice, if we knew
1 The actual probability 2 The expected return (which reﬂects risk premia) we could compute the risk-neutral probability. What about the security that pays in the “down” state?
1 Since probabilities sum to 1:
the risk-neutral probability of down is 0.74
Remember if you buy down+up you get $1 for sure and we
that assumed up costs 0.26/1.025
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- Spring '13