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mathdude2018
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Posts: 15
Joined: January 10th, 2018, 4:35 pm

Returns and volatility of spread portfolio (pairs trade)

May 18th, 2020, 3:35 pm

This is a real life trade situation where there is no margin requirements due to bilateral nature of the deal.

At all periods in time, I have to two assets A, B in my portfolio of quantity 1 each.

Day 1:
Stock A is at $100
Stock B is at $101
SpreadAB = $1

Day 2:
Stock A is at $110
Stock B is at $101
SpreadAB = $9

Calculations:
Stock A returns = 10%
Stock B returns = 0%
Portfolio returns = (10% - 0%)/2 = 5%

But for calculating the volatility of portfolio I need to find weights of A and B in portfolio, what are the weights for A and B in such spread portfolio.

I intend to use the formula:

w_A^2 * Sig_A^2 + w_B^2 * Sig_B^2 - 2*rho_A_B * w_A * w_B * Sig_A*Sig_B
 
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bearish
Posts: 5186
Joined: February 3rd, 2011, 2:19 pm

Re: Returns and volatility of spread portfolio (pairs trade)

May 18th, 2020, 4:50 pm

I sure hope you are not serious about this being a “real life trade situation”, since nothing you say about it makes sense. The simple return on your (long) portfolio is not 10% but approximately 9.95%, but that’s probably the least of the issues here. Your formula and language suggest that you are interested in a long-short portfolio, but we are at best missing some key information here.