Monday, December 30, 2013

A.W. Jones - The Original Hedge Fund

Measuring Market Risk
Jones was light-years ahead of both Wall Street practitioners and the academic community in developing an understanding of market risk as well as the relationship between individual stocks and the market. Before the academic community had codified the Capital Asset Pricing Model (CAPM) with its notion of Alpha and Beta, Jones had developed his own measure of market risk and how individual stocks related to the market. Even more astonishing is that he was actively managing the exposure of a risk-adjusted portfolio with this system.

Jones calculated a metric for each stock called Relative Velocity, which is closely related to the CAPM's Beta (the key difference being the omission of the risk-free rate in the calculation of Velocity). Relative Velocity was the tendency of a stock, based on historical performance, to move with the S&P 500 to a greater or lesser degree. Armed with this metric, the firm could then calculate to what extent its long book and short book were correlated with market moves. What follows below is an excerpt from the 1961 Basic Report to the Limited Partners of the firm, describing in detail the measurement and management of market risk.

From the 1961 Basic Report to the Limited Partners:

This is our post-graduate course. It should be taken by all partners and must be taken by those who wish fully to understand our bi-monthly reports. 

In the main body of this communication we described our investment theories and explained at least the basis of our method. It now must be made clear that such a program cannot be put into operation without careful and continuous controls. We have developed methods which provide accurate measurement of the degree of risk being taken at all times as well as a system of allocation by which we determine whether our gains or losses are attributable to stock selection or to the trend of the market. Daily computations using this method enable us to see where we stand and permit us to plan any desirable changes with regard to market risk. In addition we have a moving record of our accomplishments in market or stock-selection judgment. 

Relative Velocity
Different stocks habitually move up and down at different rates of speed, and hedging $1,000 worth of a stodgy stock against $1,000 worth of a fast mover would give no true balance of risk. We must therefore compute the velocity of all our stocks, both long and short, by their past performance, compared with the past performance of a good measure of the market as a whole. For this we use Standard and Poor's 500 Stock Index, which we consider the most scientifically constructed of the several averages. We shall refer to it below merely as the Standard 500. 

We measure, for example, the size or amplitude of all the significant swings in the price of Sears Roebuck since 1948 against the corresponding swings in the Standard 500 and find that the average extent of these moves is 80 per cent of the average extent of the moves of the Standard 500. We say therefore that the Relative Velocity of Sears is 80. 

By the same measurement (which we have made and which we bring up to date at about two-year intervals for over 2,000 stocks ) we find that the velocity of the stock of General Dynamics is 1.96. Obviously, to buy and sell short, respectively, equal dollar amounts of Sears and General Dynamics would constitute no true hedge. Instead there would have to be more than twice as much of the stable Sears stock as of the volatile Dynamics to cause them to offset each other in market risk. 

To illustrate :

This would seem to be no hedge at all, but appearances change when we correct each dollar amount by the respective velocities of the two stocks:
It must be pointed out that relative velocity has nothing directly to do with the desirability of a stock. All a velocity measurement does for us is to measure one aspect of the risk we are taking when we buy it or sell it short. Either Sears or General Dynamics might be a good purchase or a good sale, depending on all the factors that go into stock selection. From here on all the amounts used in the various examples of aggregate stock holdings will be dollar amounts after correction for velocity.

Since the Standard 500 is composed mostly of the big "blue chips," which move slowly, a portfolio of stocks commonly used for investment by us will have an average velocity over 100. Thus a list of typical stocks worth $70,000 to $80,000 in cash, might come to $100,000 after correcting for velocity (cash times velocity in each individual stock.) 

Measurement of Results 
Let us now take the simplest of cases -- a fund of $100,000 equity or net worth, with $100,000 of long positions and $100,000 of short positions (each position computed in cash times velocity.) Such a fund, being fully hedged, has a market risk of zero and all net gains or losses will be attributable to good or bad stock selection, none to the action of the market. 

For six months we maintain this even balance between long and short (this could hardly happen in actual practice,) though we shall certainly make shifts during the period within both the long and short list, thus realizing profits and losses, and then replacing the long stocks sold and the short stocks covered. Every day from the newspaper stock tables we calculate our gains and losses, arriving at a net figure for the long list and a net figure for the short list. These two figures are kept cumulatively and include both unrealized and realized gains and losses. By the end of six months, the following has happened: This is fine as far as it goes. It tells us that we have made $7,000 by good stock selection (since we are fully hedged), but it doesn't tell us how to allocate the gain as between long and short selection—perhaps we should have made more on the long side, in the market rise, or perhaps lost less an the short side. So the following further calculations are necessary: 

1) Just to keep pace with the "market" rise of 5%, our long stocks, worth $100,000 should go up by $5,000. But in fact they went up by $9,000. The difference, attributable to good long stock selection, is $4,000. 

2) Also to match the rise in the market, our $100,000 worth of short stocks should have gone up, showing us a loss of $5,000. Actually they went up only $2,000, and the difference, due to good short stock selection, is $3000.

3) For a total gain, to account for the net gain shown above, of $7,000. 

With an Unhedged Balance 

When we are not fully hedged, but have a net-long (as is usually the case) or a net-short balance, the operation has an added complication. Suppose now, still with $100,000 of equity, we are optimistic about the stock market, so we buy stocks worth $130,000 and sell short stocks worth $70,000. We hold this balance (though we may shift individual stocks) for one week, during which time the following happenes:
Our problem now is to allocate fairly this net gain.
Our reports go to a good many persons besides yourselves, and because we do not wish to reveal to all who receive them the size of the fund, also in order to indicate more clearly to you the change in your own partnership share, the figures for gains and losses are not stated in dollar amounts but in percentages of our net worth at the beginning of the fiscal year. Therefore if the week's results illustrated above were for the first week of the year, the report for that week would read: 

Progress : Since June 1, our fund has gained 2.1% against a gain of 1.0% in the Standard 500. On long stocks we show a gain and on short stocks a loss of 0.4%
These figures are the result of calculations made every day and kept cumulatively for the entire fiscal year. They include both unrealized and realized gains and losses for the period from the beginning of the fiscal year, and are calculated after brokerage expense and transfer taxes on all transactions that have taken place. 

The reports take into account dividends received on long stock and dividends paid on short stack. They take into account also, at monthly intervals in our cumulative reckoning, the interest we pay to banks and brokers. 

However, the reports overstate the eventual return to you, since they cannot conveniently, and do not, take into account the 20 per cent of realized capital gains paid over to management at the end of the fiscal year. Also, as the year goes on, the reports become more and more unfair in the comparison with the Standard 500 since to the latter should be added a small percentage as dividend yield. 

We used to report regularly and we still do report occasionally the amount that we are making in the hedged part of the fund alone. In the example above, the hedged part of the fund is the entire minority, or short list, ($70,000) combined with an offsetting $70,000 of the long list. The entire long list being $130, 000, the hedged part of it is 7/13 of the whole. We now find how much we have made in the hedged part by the following calculation: 
We keep this figure cumulatively during the fiscal year, reporting it also as a percentage (in this case 0.9%) of our equity. By a somewhat complicated method we calculate from it what we make on the hedged part of the fund as a percentage of the money actually used in it. This is a gain obtained without risk due to the trend of the stock market, and not to be had by any other form of investment procedure. 

The Risk Figure 
In the Market Judgment section of the reports you see a number variously called the risk figure, market risk, or percentage of risk in the Standard 500. From the above it is easy to see how this is obtained. Remember that our list of long stocks aggregates $130,000 only after the cash value of each stock in it has been multiplied by its velocity, relative to the Standard 500. This relates our long stocks to the Standard 500, so that $130,000 long gives us a risk on the long side alone (our equity being $100,000) of $130,000 divided by $100,000, or 1.3. Instead of using a decimal fraction we use a percentage and say that our long side risk is 130. By the same reasoning, our short risk, also exactly related to the risk in the "market", or Standard 500, is 0.7, or 70 per cent. Our net-long risk is therefore 60 (130 minus 70), which means that our net-long risk in the stock market is equal to 60 per cent of the risk we would be taking if we had our whole equity exactly invested in the stocks of the Standard 500. 

Any minus figure will stand for a net-short balance, in which we gain from a decline in the stock market. At plus 40, say, we would be incurring about the market risk of a widow with half her money in somewhat stodgy, blue-chip common stocks and half in bonds. At plus 100 to 150 we would be taking the risks of a business man with most or all of his capital in more volatile stocks. 

Containing, as it does, the velocity measurements of all of our stocks relative to the Standard 500, the risk figure is a very precise measurement of just what we want to measure. It enables us to adjust our position in the market exactly to our outlook for its probable future trend.

A.W. Jones - The Original Hedge Fund 

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