Tuesday, 15 November 2016

Scissors, a reference portfolio and a clear correlation divide

The Moves Like Jagger model (MLJ) is a kind of look inside a behaviour.  The look inside in effect chops the behaviour in two.  It acts like a pair of scissors.  All it needs is a reference behaviour.  The scissors then chop any to-be-analysed behaviour into two pieces.  One is perfectly correlated to the reference behaviour.  The other is perfectly uncorrelated with the reference behaviour.

All that the capital asset pricing model (CAPM) adds is a statement that the behaviour of the reference is worthwhile, indeed the ideal behaviour.  CAPM in effect adds morality to the scissors.  It claims that you can't act better than the reference behaviour.  A consequence of this is that the uncorrelated behaviour is in some sense wrong, sinful if you like.  Why would you do it if the ideal behaviour is to be strived for?  By making the ideal behaviour a target, you start then to see the uncorrelated behaviour as distorting, wrong, avoidable, residual.  So the language of leftovers or residua enters.

When we finally get to the equity factors active management approach, a space again opens up to re-analyse the so-called residua into a superlative component and a random component.  The superlative component is behaviour which is actually better than the reference behaviour.  FInally after this better behaviour is analysed (it is called alpha), it is claimed that the remainder is once again residua.

The scissors operation of covariance is the tool.  CAPM is the use of the tool in a context of some assumptions around the perfection of the reference behaviour.  Post-CAPM/equity factors is the use of the scissors in the context of some assumptions around the possibility of exceeding the quality of the reference behaviour.

One aspect of CAPM I have not spent much time on is the element of risk appetite.  Let's pretend that the only asset available to you is the Vanguard market ETF and that you have 1 unit of capital which you've allocated to investing.  No sector choices are possible.  No single name choices are possible.  Are you limited to receiving on average just the market return?  No, because there's one investment decision you need to make which is prior to the  CAPM, namely how much of your investment unit you'd like to keep in cash and what fraction you'd like to invest in the market.

The way you go about that decision is an asset allocation decision, and is a function of your appetite for risk, which is said to exist prior to the CAPM reasoning.  If you have no appetite for risk you invest precisely 0% of your unit capital in the market portfolio (and receive in return the risk free rate).  In theory, you could invest 100% of your unit of capital and receive the market return.  Indeed, in theory you can invest >100% of your unit of capital, through the process of borrowing (funding leverage) or through the selection of assets witg built in leverage (asset leverage).  Through either of these techniques, or any combination of both, you can get a return which is an amplified version of the market return. 

With amplified returns though, or gearing, you run the risk of experiencing gambler's ruin early in the investing game.   Gambler's ruin traditionally happens when the capital reduces to 0.  Its probability can be estimated.  With any kind of amplified return, there's a point before 0 where your broker, through margin calls, will effectively bring the investing game to a halt.

The process by which you decide what your degree of investment and amplification in the market is going to be is an asset allocation decision.  You're after all investing your unit either in the market portfolio or in the risk free asset.  This decision can be made once forever.  What is the single static best allocation of cash between the risk free asset and a correspondingly over-or under-invested market portfolio?  Or this decision can be time sensitive - i.e. your decision can move with time.

Insofar as the investment community does this in a more or less correlated way this creates waves of risk-on and risk-off patterns in markets. 

Making a single fixed static allocation decision is a bit like a surfer who bobs up and down in a stationary way as waves arrive to the shore.  Trying to be dynamic about it is like that same surfer standing up at some point and trying to let that wave take him to shore on a rewarding ride.  The CAPM in a sense tells you nothing about which of these two approaches are best for long term returns.