Calculating Arbitrage Strategy - PM Multi Factor Models

CFA Level II
#1

Hi all,

What is the quickest way to find out the correct weightings of the factor sensitivies to replicate a portfolio.

Say:

Portfolio A: ER = 10% Fac Sens = 1.2

Portfolio B: ER= 20% Fac Sens = 2.0

Portfolio C: ER=13% Fac Sens = 1.76

How can I quickly compute what weightings are needed to give a factor of 1.76? (In this case 70% A, 30%B). I am currently just trying trial and error.

Thanks

#2

You mean 70% B and 30% A?

Normally if the answer provides 3 weightings, trial error is the best strategy to see which answer choice fits.

#3

Yes- 70%B, 30% A. The problem is that the question is unlikely to be ‘calculate the weightings’.

The question here was calculate which portfolio to go long and short in. We must first calculate the weightings to get the New portfolio D. I am not sure how in the exam you can quickly work out what weights are needed to replicate the 1.76 in the example above.

Can anyone else help?

#4

(This is QUestion 2 Schweser EOC p164)

#5

What I mean is that the answer will have three choices.

  1. Long A 20% long B 80%

  2. Short A long B

  3. etc etc

Check one by one to see which answer fits. Your trial error will take maximum 2 errors and should be easy and quick.

#6

Also check this

http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91349452

#7

With all due respect, no it isn’t.

There was another thread on this very subject.

(That’s the one!)

The analytical approach is:

  • Identify the portfolio with the highest sensitivity and the portfolio with the lowest sensitivity
  • Calculate the weights of those portfolios that will give a portfolio that matches the sensitivity of the third portfolio
    • The weight on the highest-sensitivity portfolio will be (middle sensitivity − low sensitivity) / (high sensitivity − low sensitivity)
    • The weight on the lowest-sensitivity portfolio will be (middle sensitivity − high sensitivity) / (low sensitivity – high sensitivity)
  • Use those weights to determine the expected return on the new, composite portfolio
  • Compare that return to the expected return of the middle portfolio
  • If they’re equal, no arbitrage opportunity
  • If they’re unequal, buy the portfolio with the higher return and sell the portfolio with the lower return

Here, the weights are:

  • (1.76 – 1.2) / (2.0 – 1.2) = 0.7 for portfolio B
  • (1.76 – 2.0) / (1.2 – 2.0) = 0.3 for portfolio A

The expected return on the A/B composite portfolio is:

0.7(20%) + 0.3(10%) = 17%.

As portfolio C’s return is 13%, you sell (short) portfolio C, and buy 30% A/70% B.

#8

BILL STRIKES AGAIN! Love it. I assume that this method can be used for any facot sensitivites?

Will check the other thread too.

Thank you!

#9

Yup.