Actuarial Outpost > SoA Fall 2005 8E #3c
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#1
04-28-2008, 03:14 PM
 Chance123 Member Join Date: Aug 2006 Posts: 153
Fall 2005 8E #3c

I feel like the solution is incorrect. They are using the same formula/values to solve for the risk-neutral probability and the expanded NPV. It's like saying 1=1. I think the only reason they're getting 0.04 instead of 0 is due to rounding. Does anyone know how to solve this correctly? Thanks!
#2
04-28-2008, 05:58 PM
 inexactuary Member SOA AAA Join Date: Apr 2006 Location: OH Favorite beer: Newcastle Posts: 569

Quote:
 Originally Posted by Chance123 I feel like the solution is incorrect. They are using the same formula/values to solve for the risk-neutral probability and the expanded NPV. It's like saying 1=1. I think the only reason they're getting 0.04 instead of 0 is due to rounding. Does anyone know how to solve this correctly? Thanks!
Agreed. The correct approach would be to use the 8% to find the value of the project w/o the option: (.5*2150+.5*600)/(1.08)^5=935.80. Then use this to find the risk-neutral probability of going up: [935.80*(1.04)^5-600]/(2150-600)= 34.74%. Finally, you can apply the risk-neutral probabilities to New West's share of the project with buyout option: [1600*.3474+300*(1-.3474)]/(1.04)^5-600=17.8.
#3
04-28-2008, 08:28 PM
 Chance123 Member Join Date: Aug 2006 Posts: 153

I generally agree with your approach, inex. The only modification I would make is to substitute the 2150 with 1075 and 600 with 300 (since that is New West's share). This affects the calculation for the passive NPV in part b, for which I got a value of -132.10. Using the 1075 and 300 gets the same p of 0.3474 (because the 50% cancels out).
#4
04-29-2008, 08:29 AM
 inexactuary Member SOA AAA Join Date: Apr 2006 Location: OH Favorite beer: Newcastle Posts: 569

Quote:
 Originally Posted by Chance123 I generally agree with your approach, inex. The only modification I would make is to substitute the 2150 with 1075 and 600 with 300 (since that is New West's share). This affects the calculation for the passive NPV in part b, for which I got a value of -132.10. Using the 1075 and 300 gets the same p of 0.3474 (because the 50% cancels out).
Our approaches are equivalent since the two companies have proportionate shares in the projects value (they are like twin securities of each other!). I agree that you certainly need to just look at New West's share for part b.
#5
04-29-2008, 08:36 AM
 inexactuary Member SOA AAA Join Date: Apr 2006 Location: OH Favorite beer: Newcastle Posts: 569

Quote:
 Originally Posted by BTBU Well, referring to the past exam 8E-2006-2. It is given that the initial value of the twin security is 100 and the value at time 4 is (174.90,52.20). Do you find that these are not consistent with Beta 1.50 (That is, risk-adj discount rate 15%) and Real Prob(up)=0.55, Real Prob(down)=0.45? (174.90*0.55+52.20*0.45)/1.15^4=68.43 Also, I test (174.90*0.55+52.20*0.45)/1.15^1=104.07(Assume that Beta corresponds to 4yr risk rather than 1yr risk. This seems strange, but just a test.)
You are correct, the twin security and CAPM assumptions are not consistent. In addition, the twin security is not even proportional to the project values. I would just ignore the twin security paragraph altogether. My guess is that it was part of an earlier version of the problem and they forgot to take it out.
#6
04-29-2008, 10:24 PM
 phdmom Member SOA AAA Join Date: Nov 2001 Posts: 293

Quote:
 Originally Posted by BTBU As well, I have question about past exam 8F-2002-11. Still about the Beta and the risk-adj discount rate. Disregarding the option to defer, the Beta of the project is 1.5 and the risk-adj discount rate is 15%. Now add the option, is the project of the project with option still with Beta 1.5 and Discount rate 15%? It should not because the risk has changed. What's stranger in the model solution, the Q-measure characteristics are based on the Project with option. I don't think it correct. The Q-measure characteristics should be calculated from the project w/o option. That is the project with ending value at time 1 (397.43,298.40 50%,50%).
I was confused why the reduced cash flows were discounted to time 1, if it is an option to defer for 2 years. I hadn't thought if the discount rate should be different or not.

So you are saying, take the original cash flows discounted at 15% and find the risk-neutral probability. Then use it and the risk-free rate to discount the reduced cash flows. To what time? Do we assume time 1 is one year after investment, whether that's 1 or 3 years from now?

Quote:
 Originally Posted by BTBU Heavy headache with those past exam questions in 8F and 8E, except 8F-2002-5 which is consitent with my understanding.
Me too!
#7
04-30-2008, 05:31 PM
 phdmom Member SOA AAA Join Date: Nov 2001 Posts: 293

Quote:
 Originally Posted by inexactuary You are correct, the twin security and CAPM assumptions are not consistent. In addition, the twin security is not even proportional to the project values. I would just ignore the twin security paragraph altogether. My guess is that it was part of an earlier version of the problem and they forgot to take it out.
(Referring to 2006 8E #2).

So, rather than the twin security, use part b to find the risk-neutral probability. (The cash flows of the project without the option). Then figure out the cash flows if the option is exercised, apply the risk-neutral probabilities and discount at the risk-free rate? I'm getting a more negative NPV this way (so the option has no value?)

I struggle with these. Each example of this type of problem I see, it seems like I need a different approach to solve it & I don't see why.
#8
05-01-2008, 11:02 AM
 inexactuary Member SOA AAA Join Date: Apr 2006 Location: OH Favorite beer: Newcastle Posts: 569

Quote:
 Originally Posted by phdmom (Referring to 2006 8E #2). So, rather than the twin security, use part b to find the risk-neutral probability. (The cash flows of the project without the option). Then figure out the cash flows if the option is exercised, apply the risk-neutral probabilities and discount at the risk-free rate? I'm getting a more negative NPV this way (so the option has no value?) I struggle with these. Each example of this type of problem I see, it seems like I need a different approach to solve it & I don't see why.
To calculate the value without the options, you have to discount the year two expense at the risk-free rate, not the risk-adjusted rate.
#9
05-01-2008, 11:32 AM
 phdmom Member SOA AAA Join Date: Nov 2001 Posts: 293

Yeah, that helped.

So I set up this equation:

(.55 * 8,121,500 + .45 * 2,837,000 - 2,000,000)*1.15^(-4) = (p*8,121,500 + (1-p)* 2,837,000 - 2,000,000)*1.06^(-4)

Solving for p, I get .279 which is still smaller than the solution's p of .3965 (using the twin security cash flows), but does give a reasonable answer for the value of the project including the options (higher than the value without).

I had ignored the 2,000,000 on both sides of the equation before, forgetting that they don't exactly cancel.
#10
05-01-2008, 12:34 PM
 inexactuary Member SOA AAA Join Date: Apr 2006 Location: OH Favorite beer: Newcastle Posts: 569

This is actually what I had in mind (where they do cancel), but I think both ways are defensible, depending on whether the 15% corresponds to the gross value or net value in two years.
(.55 * 8,121,500 + .45 * 2,837,000)*1.15^(-4) - 2,000,000*1.06^(-4) = (p*8,121,500 + (1-p)* 2,837,000 - 2,000,000)*1.06^(-4) - 2,000,000*1.06^(-4)

I think what you were doing before was calculating the risk-neutral from this equation, but when you calculated the value w/o the option, you discounted the 2,000,000 at the risky rate, not the risk-adjusted rate. This is inconsistent with how the risk-neutral probs were calculated.

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