Delta of portfolio?

[ajsa]

Hi David,

Is the delta of portolio the weight avg of delta each options with the same underlying? What weight would we use? The option's market value? or underlying's market value?

thanks.

 

[David Harper CFA FRM]

Hi asja,
Yes, if the underlying is the same, the delta is a simple weighted average and the weight is the quantity (N) of options.
(if the underlyings were different, the "value delta" would be needed which does use the market value of the underlying, but for the same underlying, the market value of underlying is not needed to aggregate delta)

Carol Alexander (Vol III, Market Risk analysis) uses helpful terminology:
delta = "percentage delta" (although delta is technically unitless, it still may be helpful...), and here is the term i like
position delta = percentage delta * Number of options

so, if you consider the example of Hull's making the position gamma neutral
see http://www.bionicturtle.com/premium/spreadsheet/4.b.9_gamma_neutral/

the first column is Hull's example of a portfolio that's delta neutral with gamma of -3,000
(and his usage here requires the same underlying...)

that is a portfolio with a position Gamma of -3,000 and he wants to make it delta and gamma neutral

so his first trade is long 2,000 call options with percentage delta of 0.62
such that 2,000 quantity * percentage delta 0.62 = position delta of 1,240

then second trade gets to delta neutral by shorting 1240 shares; i.e., -1240 * percentage delta 1.0 = position delta of -1,240

while that's not what you asked exactly, you can see that for a portfolio of same underlyng, the same idea applies:
since the portfolio simply ADDS position deltas, the portfolio delta is (simply) the component deltas weighted by quantity (N)

David