Question about example in Copeland

[hamstrman]

So this is driving me crazy for no other reason than I'm actually crazy about solving math problems.

Chapter 9 of the Financial Theory and Corporate Policy has an example, in the "Switching Options" section, that discusses how to value two options with the flexibility to switch between them.

Cash flows for Asset X grow at 1.4 (u = 1.4, d = 1/u). For Asset Y, it's 1.1 (u = 1.1, d = 1/u)

Cost of Capital = 9%, rf = 5%

Real-world probabilities, p and 1-p are 0.5 for both X and Y.

They use a replicating portfolio to get the value of asset Y so that arbitrage cannot occur...

mX + (1.05)B = Y

For example, for the upper node and middle node:

m (196) + 1.05B = 121
m (100) + 1.05B = 100

So my question is (obviously you will have to have read this to help, I didn't type the whole problem out...) how do they get the value, at time 0, for asset Y of 285.85 (which includes the $100 cash flow at time 0)? I can match every other number on the tree of values, for both X and Y except this last number. What replicating portfolio do you need to get this last value?

Along the same lines, how do they get the value of 305.3 (again including the $100 cash flow at time 0)for the hybrid when starting in Mode Y? This is the essentially the same problem that I am having in both places. Any help would be greatly appreciated!

[britta]

I was working on it too and couldn't get the numbers to match - the differences aren't big but they're too big for rounding errors.

I wouldn't waste any more time on it if you get the other numbers right; there are other annoying errors in the chapter, like the value of the expansion option at the bottom of page 319, and the omission of discounting on page 332 (as noted in the JAM manual).

What still confuses me is why the relationship between p, u, d and k doesn't hold for the switching options example - but again, I think I understand the method so I don't plan on losing any sleep over it.

[hamstrman]

Originally Posted by britta

I was working on it too and couldn't get the numbers to match - the differences aren't big but they're too big for rounding errors.

I wouldn't waste any more time on it if you get the other numbers right; there are other annoying errors in the chapter, like the value of the expansion option at the bottom of page 319, and the omission of discounting on page 332 (as noted in the JAM manual).

What still confuses me is why the relationship between p, u, d and k doesn't hold for the switching options example - but again, I think I understand the method so I don't plan on losing any sleep over it.

Thanks so much. I asked a coworker to try solving it independently and they matched my numbers exactly (also different from the book). I have since moved on, but it was just driving me crazy, I needed someone to tell me they couldn't get it either but felt confident that they were doing it right.

[FrankieY18]

Can someone explain to me why they use realistic probabilities instead of risk-neutral?

[mlschop]

Originally Posted by FrankieY18

Can someone explain to me why they use realistic probabilities instead of risk-neutral?

As long as you are using all risk free or "realistic" assumptions, I think both are supposed to come out with the same results, no?

In terms of building binomial trees, use risk free rate if you are using risk neutral probabilities, and use the WACC if you are using non-risk-neutral probabilities.

[hamstrman]

Just in case anyone else encounters my original issue, the answer is they won't match. The method of discounting is the same at all nodes as is the method for creating replicating portfolios. I don't know what they're rounding to get such ridiculous rounding errors, but "rounding error" is their way of saying, "we don't feel like explaining it to you".

[FrankieY18]

Originally Posted by mlschop

As long as you are using all risk free or "realistic" assumptions, I think both are supposed to come out with the same results, no?

In terms of building binomial trees, use risk free rate if you are using risk neutral probabilities, and use the WACC if you are using non-risk-neutral probabilities.

I think what you are saying is only true if manager pre-commits the project...if there is option (i.e option to expand, option to abandon, etc.), then we cannot use WACC to discount because of the risk profile of the project would be different...therefore, we should use risk-free rate and risk neutral probabilities...

btw, side question...you use risk-neutral probabilities to hedge or real probabilities?