In a September post I suggested that Warren Buffett had no grasp of option delta (sensitivity of option price to changes in the market). A number of people have privately challenged me on this. Buffett is a smart guy, any smart person understands option pricing, ergo etc.
On the contrary.
Here are the relevant sections of Buffett’s 2010 newsletter.
Both Charlie and I believe that Black-Scholes produces wildly inappropriate values when applied to long-dated options. We set out one absurd example in these pages two years ago. More tangibly, we put our money where our mouth was by entering into our equity put contracts. By doing so, we implicitly asserted that the Black-Scholes calculations used by our counterparties or their customers were faulty.
We continue, nevertheless, to use that formula in presenting our financial statements. Black-Scholes is the accepted standard for option valuation – almost all leading business schools teach it – and we would be accused of shoddy accounting if we deviated from it. Moreover, we would present our auditors with an insurmountable problem were we to do that: They have clients who are our counterparties and who use Black- Scholes values for the same contracts we hold. It would be impossible for our auditors to attest to the accuracy of both their values and ours were the two far apart.
We believe the true liability of our contracts to be far lower than that calculated by Black-Scholes, but we can’t come up with an exact figure. [/indent]
As I argued in the post, Buffett must be assuming that the mark to market B-S option p/l, i.e. the one auditors insist on, is imaginary. He ‘nevertheless’, i.e. notwithstanding that it is incorrect or imaginary, uses it for valuation to avoid accusations of shoddy accounting. He uses it because he is forced to, and he is quite explicit that ‘Black-Scholes calculations used by our counterparties or their customers were faulty’ (my emphasis).
It logically follows, if the B-S valuation itself is faulty, that B-S delta, i.e. the sensitivity of that same valuation, is faulty.
But as I argued, it surely follows that the delta of the synthetic long position obtained by adding a long call option struck at the same level as the short put option, must be faulty also. Yet the synthetic has an identical value to buying the underlying at 100, since it pays off the same in every possible circumstance, and then it would be quite wrong to ignore the P/L swings on the synthetic, given that you should not ignore them on the real asset. The auditors would object to the one case, just as they would to the other.
As for the premium on the put option that Buffett thinks is undervalued, note this this disappears when we add the long call position, for one premium cancels out the other. This suggests what the premium is for. The problem of a short put position is that its delta falls as the market rises. As the market continues to rise, you get less and less of a profit from your long position, compared to the profit of a position in the asset itself. (Correspondingly as the market falls, you get more and more of a loss). Towards expiry – as delta approaches zero – there is no profit at all. Adding the long call corrects that problem, but of course you have to pay the premium to do that, and that is precisely what the premium is for.