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Name: Brian Hird
Affiliation:
E-mail: brian-h@usa.net
Date: 31 Aug 1997
Time: 15:51:04
I haven't posted previously on this topic because it is complex and cannot be dealt with in just a few lines. If anyone wants to raise any points with me personally by e-mail, feel free - but only if you've thought about it VERY CAREFULLY first.
There are 2 basic RAPM schools of thought: - VaR-based techniques - Sharpe ratio techniques, by which I mean "average P&L / standard deviation of P&L" type measures value-at-risk techniques are, in my opinion, appropriate for this problem and are complementary to Sharpe ratio techniques for this reason: Sharpe ratio techniques are purely backward-looking. It is not possible to do any forward planning with a Sharpe ratio - more on this in section 3.
Anyway, here goes for my thoughts on RAPM and value-at-risk:
1) If you want to use Risk-adjusted Performance Measures you must begin by asking yourself these 2 questions: - what is meant by performance? - what is meant by risk?
2) Performance
Performance is only partially measured by profit and loss statements - contrary to what 99% of traders seem to believe. My view of a business - any business, whether it is a bank or a company which makes nuts and bolts - is quite simple:
It is a black box into which you put money ("capital") and from which you get money back ("return"). "Return" is cash. "Capital" is money raised by issuing equity - neglecting debt issuance for simplicity. Those shareholders require a return for investing their money in your company.
This is the logic behind the use of the Return on Capital Employed ("ROCE") by financial analysts e.g. equity analysts and corporate financiers.
Return on Capital Employed is therefore a better measure than many e.g. Return on Assets, or the cost-income ratio so (mistakenly in my opinion) beloved by some banking sector analysts and management accountants. However ROCE is not the whole story. Why? Because seeking to maximise ROCE is not necessarily correct.
Forget the issue of risk adjustment for the moment. Say I am a trader and my average return on capital is (on trades to date) 25%. I am now looking at a marginal trade with the same risk level as the average level of risk in my trades to date. This trade has a return on capital of 20%. If I am seeking to maximise my return on capital, I would pass up the trade as it reduces my overall ROCE.
Whether you should do the trade or not depends solely on whether it "creates" or "destroys" shareholder value. That is, if my cost of capital is 17%, then I should do the trade - because it is generating a greater return on capital than that required by those who have provided me with my money - shareholders - in the first place. If my cost of capital is 23%, I should not do the trade because I am generating less return per unit capital than it has cost me to raise that capital in the first place.
Assessing the appropriate discount rate is core to equity valuation by discounted cashflow (DCF). I won't go into this since any good (non-markets) finance textbook will outline this e.g. "Principles of Corporate Finance" (Brealey & Myers) or "Valuation" (Copeland, Koller & Murrin).
3) Risk
WHat do we mean by "risk"? A detailed examination of what we mean by "value-at-risk" may give us a clue. value-at-risk is defined to be the m'th-percentile confidence interval for mark-to-market P&L generated by market moves on a set of positions static over an n-day holding period. No big deal - we all knew that.
But let's focus on 2 parts of that statement in particular: - "generated by market moves" and - "a set of positions static over an n-day holding period"
The return on a trading book is generated through many different sources, of which MTM P&L from market movements is only one. What about money earned from taking on credit risk? This is, after all, the core of retail and commercial banking. What about brokerage fees? What about customer flow income i.e. the market-maker's bid-offer spread. I could go on, but these serve to illustrate the point.
We can characterize each of these as "risk factors" or "revenue streams". Each is a random variable - i.e. any given outcome for each of these factors (which is what we see aggregated in the overall P&L number for a given trading book) is only one of a large number of possible results for that risk factor.
This implies we need to broaden our concept of what "risk" is in order to fully implement a RAPM. This is one big problem that I have with Sharpe ratio techniques on their own: what does a times series of these numbers mean if the mix of risk factors in your P&L is continually changing? How do you "optimise" on the basis of these numbers?
A final thought on performance: we need to measure P&L on the same basis between risk factors. Predominantly "banking books" are traditionally accrued rather than marked to market whilst the reverse is true in the case of most trading books. Yet elements of both P&L streams appear in many books. It is posible to MTM an accrual book; it is not really possible to MTM a trading book. The big problem of course is to adjust the realised MTM P&L for future expected losses i.e. get your credit reserving correct - accrual accounting is used on books which generate most of their income from credit risk for this very reason - in order to side-step the issue of credit reserving.
If we regard each risk factor / P&L stream (2 terms for the same thing) as a random variable whose distribution we are trying to characterise - perhaps in just the first 2 moments, perhaps in more - life becomes a lot clearer: For each risk factor characterise the distribution i.e. (a) adjust the P&L so that it reflects expected future losses i.e. so that the distribution is correctly "centred" (b) estimate the dispersion of the distribution (c) take account of the correlation between these risk factor distributions to generate a joint distribution of E(aggregate P&L) [where E() is the expectation operator] and your estimate of a confidence interval on that distribution. The latter is an estimate of how much your aggregate P&L can fluctuate.
4) Combining Return and Risk
From another perspective, the extent to which our P&L can fluctuate is an estimate of the capital buffer required to support that business - i.e. how much money we need to set aside in order to allow the business to keep trading under all but very unlikely conditions - exactly which conditions being a function of the confidence interval we have used.
This capital is not free - obviously. We should therefore charge ourselves the cost of raising this additional "buffer capital" as well as on the cost of raising capital used for other purposes (working capital). This cost is the rate of return which our shareholders require for providing us with capital.
Almost there now - as with ROCE, this is the general logic behind RARORAC (risk-adjusted return on risk adjusted capital). However RARORAC, as it is a *ratio*, suffers the same problem as ROCE - i.e. you shouldn't run around trying to optimise it.
Economic Value Added (EVA) [sometimes also called Shareholder Value added (SVA)] = MTM profit after adjusting for any future expected gains or losses not yet recognised and after deducting the opportunity cost of capital is the true return we have provided to our shareholders in this accounting period
If our actions this accounting period do not affect future accounting period EVA's, then 1-period EVA is what we shouold be aiming to maximise.
It is possible (but I've run out of steam) to combine a forecasted time series of numbers adjusted on this basis to calculate a risk-adjusted shareholder value number.
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