P2 Instructional Video: Bodie, Chapter 24

[CFO2013]

Hello,

Can you please explain how you arrive at the formula using the call option approximation for the market timing effect. I believe this formula appears at 20 minutes and 36 seconds after the start of the video. Thanks in advance for your help.

 

[David Harper CFA FRM]

Hi @CFO2013 I think you refer to Bodie's formula 24.6:

"Because the ability to predict the better-performing investment is equivalent to holding a call option on the market, in any given period, when the risk-free rate is known, we can use option-pricing models to assign a dollar value to the potential contribution of perfect timing ability. This contribution would constitute the fair fee that a perfect timer could charge investors for his or her services. Placing a value on perfect timing also enables us to assign value to less-than-perfect timers. The exercise price of the perfect-timer call option on $1 of the equity portfolio is the final value of the T-bill investment. Using continuous compounding, this is $1 * exp(rt). When you use this exercise price in the Black-Scholes formula for the value of the call option, the formula simplifies considerably to: MV(Perfect timer per $ of assets) = C = 2N[0.5*σ(M)*sqrt(T)] - 1"

So *apparently* if we assume S = 1 and X = e(rt), then BSM call option (c) = S*N(d1) - K*exp(-rT)*N(d2) simplifies to C = 2N[0.5*σ(M)*sqrt(T)] - 1. (I haven't checked it but appears reasonable given the canceling it implies). I hope that helps, thanks,

 

[CFO2013]

This is indeed correct, d1 = (0.5*σ(M)*SQRT(T)) and d2 = d1-σ(M)*SQRT(T) = -0.5*σ(M)*SQRT(T) = -d1. Therefore, C = N(d1) - N(-d1) = 2N(d1)-1
Many Thanks again David for your help.

 

[David Harper CFA FRM]

Oh, yes, I see now, very cool, thank you!

 

[Shau_2207]

Hello All, Can anyone please help an example?

 

[gsarm1987]

Hello All, Can anyone please help an example?

@Shau_2207 which example?

 

[Shau_2207]

I found an example of MV(Perfect timer per $ of assets) in GARP book see attached but i am not able to figure out the working or calculation 2N, do we need to multiple N value , is the N value right tail or left tail?

Can you please help?

 

[gsarm1987]

@Shau_2207 This expression is a result of simplification. Please see David's comment above (april 17 and 18, 2014). In short, equity is a call option on asset.

starting point: S(V,F,T,t) = VN(d1) - Pt(T)FN(d2).
on page 238/340 of your ebook (BT notes), you will see it is using an analogy that market timing is just like holding a call option