[Fin525sp09] Sample Midterm problem #3

[d.tomaszewski at comcast.net]

Good morning Professor.  Is it possible for you to post the solutions for the 17 problems that you posted last week?  


----- Original Message ----- 
From: "Eishita Shah" <eishita at live.com> 
To: fin525sp09 at mailman.depaul.edu 
Sent: Monday, April 27, 2009 9:34:06 AM GMT -06:00 US/Canada Central 
Subject: [Fin525sp09] Sample Midterm problem #3 


Hello Professor, 

For problem 3, we are given sensitivity coefficient (B) and Expected 
returns E(r), however to use two portfolios to derive at the common 
factor (m) for this one-factor model, we still need a remainder risk (alpha). Then using the factor, we derive at security retun r(i). My question is: is this alpha the same for all three equations? Only with aplha being the same, can we derive at R(m). 

How is it possible for this remainder risk to be the same for all three portfolios? Is this an assumption we make for the sake of the 
problem? 

Following are the equations I am using to derive first at R(m) and then at alpha. I am probably not using correct formulas for appropriate calculations, as my answers are incompatible with yours. 

a = alpha; m = factor 
Solving for m: 
For A: 12 = a + 2m 
For B: 15 = a + 3m 
For C: 10 = a + m 
  
I obtained m = 3, and a = 6. Using m only I solved for r(i) = E(r) + m 
For A, r(a) = 18 
For B, r(b) = 24 
For C, r(c) = 13 
  
Please Advise! 

Thanks, 
Eishita 
> > 
> > 
> > > Date: Sun, 26 Apr 2009 18:26:31 -0500 
> > > From: agehr at mozart.depaul.edu 
> > > To: fin525sp09 at mailman.depaul.edu 
> > > Subject: Re: [Fin525sp09] Question on Midterm problem #3 
> > > 
> > > You don't need a risk-free rate. All you need to do is buy and sell 
> > > portfolios which have the same factor-sensitivities. With three 
> > > securities you can find a combination of two which replicate the factor 
> > > sensitivity of the third (and it doesn't matter which you pick--you 
> > will 
> > > get the same result). Check the expected returns to find out which to 
> > > sell and which to buy. If you get the same return on all combinations 
> > > with the same factor sensitivity, you have an equilibrium. Otherwise 
> > you 
> > > have an arbitrage opportunity. 
> > > 
> > > In this example, I'd try to find the easiest way to mix 
> > > securities--combine the high and low sensitivity securities to match 
> > the 
> > > sensitivity of the middle one. Then calculate expected returns. 
> > > 
> > > Adam Gehr 
> > > 
> > > 
> > > 
> > > patrick Redmond wrote: 
> > > > Professer Gehr - 
> > > > 
> > > > I do not understand question #3 on the sample midterm; could you 
> > > > provide some information on this probem? 
> > > > 
> > > > Spcifically, how to start this problem without a Risk-free rate. I 
> > > > understand how to constitute an arbitrage, but not with the 
> > > > information provided. 
> > > > 
> > > > Thanks in advance for your help, 
> > > > 
> > > > Kevin Redmond 
> > > > 
> > > > 
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