It’s often useful in testing a theory to push it to extremes. So let’s postulate that we sell a 100- year $1 billion put option on the S&P 500 at a strike price of 903 (the index’s level on 12/31/08). Using the implied volatility assumption for long-dated contracts that we do, and combining that with appropriate interest and dividend assumptions, we would find the “proper” Black-Scholes premium for this contract to be $2.5 million. To judge the rationality of that premium, we need to assess whether the S&P will be valued a century from now at less than today. Certainly the dollar will then be worth a small fraction of its present value (at only 2% inflation it will be worth roughly 14¢). So that will be a factor pushing the stated value of the index higher. Far more important, however, is that one hundred years of retained earnings will hugely increase the value of most of the companies in the index. In the 20th Century, the Dow-Jones Industrial Average increased by about 175-fold, mainly because of this retained-earnings factor. Considering everything, I believe the probability of a decline in the index over a one-hundred-year period to be far less than 1%. But let’s use that figure and also assume that the most likely decline – should one occur – is 50%. Under these assumptions, the mathematical expectation of loss on our contract would be $5 million ($1 billion x 1% x 50%). But if we had received our theoretical premium of $2.5 million up front, we would have only had to invest it at 0.7% compounded annually to cover this – 3 – loss expectancy. Everything earned above that would have been profit. Would you like to borrow money for 100 years at a 0.7% rate? Let’s look at my example from a worst-case standpoint. Remember that 99% of the time we would pay nothing if my assumptions are correct. But even in the worst case among the remaining 1% of possibilities – that is, one assuming a total loss of $1 billion – our borrowing cost would come to only 6.2%. Clearly, either my assumptions are crazy or the formula is inappropriate.
Posts By Tagaspergers australiapropertyboom buffett chinapropertyboom concentration creativity customer development distraction drones education facebookboom food gmo google health indiarealestateboombust inequality innovation insourcing internet investingphilosophy investmentideas jobs jpmwhaletrade lbj life movies retail selfdrivingcars startupresources stormiscoming strategy tailriskboom telecom treasurybubble usrealestatebust
Posts By Category