Saturday, 27 March 2010

Diversifying: A rant about VaR

Setting your risk budget, trying to understand the 'downside' of an investment..and diversify those risks.. these are all reasonable questions when investing. In the last few years many have turned to Value at Risk analysis ('VaR') as an answer.

What is it with Value at Risk analysis... People do seem to forget how distribution stats work and the simple fact they are 'confidence' models... when talking to friends and colleagues I like trying to flip the confidence around into betting odds.. 1 in 20, in 200 etc.. this seems to give folks a better understanding of the probable (the likely 90, 95% etc) and the less probable.

Confidence: I found it hilarious that folks mistook: '1 in 200 chance of x event over 1 year, as a '1 in 200 year event'.. this is a very schoolboy error; (one prevalent across actuarial circles). Game-theorists aside: the odds of 1 in 200 are the same in every year.. the size of that risk is also not known, it falls outside our confidence (i.e. we don't know). Some reported experiencing 1 in 200 year events for the last 3 years.. clearly that's not right?!


Downside and Diversification.. VaR is used mainly for 2 things: to gauge the likely 'downside' of an investment and as a way to budget that risk. The problem is that most VaR is based on historical returns BUT what the investor gets back rarely matches the marketed standard time period returns. Once folks thought they had found someone who could but he turned out to be running a Ponzi scheme..

Let's ignore forward VaR (ex-ante, stochastic models) as that treads into forecasting and I haven't the energy to talk about crystal balls for one night!

Getting back to setting out risk for the investor - most are advised to diversify, why? The schema of diversification, and how it's presented, is so wrapped-up in spin that it's debatable science. It's the investment houses that tell us to diversify, why, because their revenue models are based around long-term assets.. tactical investing is seen as an unstable force: (i.e. bad for annual management fees). Yes - short term herding can be quite destructive and Fidelity's Magellan study showed investors rarely profited but that's down to education and of course confidence: investment houses treat customer assets as their own, once allocated. It's for the adviser and the investor to remind them otherwise, set specific investment horizons and targets.
As someone who has worked both sides of the fence: I found that financial risk and investing does not lie inside VaR or any Math model for that matter.
 
 "I can calculate the motion of heavenly bodies, but not the madness of people." Isaac Newton
The investors who seem to win more than they lose don't appear to do anything complex. They seem to start by knowing they'll lose and play the long game. In short they rely on the illogic of others to do the work for them. They play the behavioural card.
"We simply attempt to be fearful when others are greedy and to be greedy only when others are fearful." "You only have to do a very few things right in your life so long as you don't do too many things wrong." Warren Buffett
"Bull markets are born in pessimism, grow on skepticism, mature on optimism, and die of euphoria."-- Sir John Templeton
"The market can stay irrational longer than you can stay solvent."-- John Maynard Keynes

Perhaps the lessons to be learned here is not invest by looking at performance-based risk at all but by stepping back and looking at other factors involved. I hope to pick up on some of these in my new paper 'Clown Thinking and the financial Media Circus'. JB
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Quote of the day: "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence." Albert Einstein (attributed)

Investment U

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Delta changes in risk aversion (Nov09)

Sentiment: The 'Lag' Effect

Sentiment: The 'Lag' Effect
Investor perception of risk is rarely up to date

Global Consciousness Project (GCP) 'Dot'

The Global Consciousness Project collects random numbers from around the world. This is a real time data analysis of the GCP. It collects the data each minute and runs statistics on the stream of random numbers generated by the project. This analysis is run 10 minutes behind the generation of the data. In this way, it can be seen as a real-time indicator of global consciousness coherence. http://gcp.djbradanderson.com/ BLUE DOT: Significantly small network variance. Suggestive of deeply shared, internally motivated group focus. The index is above 95% BLUE-GREEN DOT: Small network variance. Probably chance fluctuation. The index is between 90% and 95% GREEN DOT: Normally random network variance. This is average or expected behavior. The index is between 40% and 90% YELLOW DOT: Slightly increased network variance. Probably chance fluctuation. The index is between 10% and 40% AMBER DOT: Strongly increased network variance. May be chance fluctuation, with the index between 5% and 10% RED DOT: Significantly large network variance. Suggests broadly shared coherence of thought and emotion. The index is less than 5% The probability time window is one hour. For a more information on the algorithm you can read about it on the GCP Basic Science page

Choosing Mutual Funds..

Choosing a Mutual Fund – CLUE “it is not about past performance.." You could try - Logic Scoring! The trick is to create your own metrics and populate them into your own grid.. Always remember to test your assumptions v outcomes: your model may be right but you may find what you thought to be a SELL is actually a BUY. Always look at the problem in the mirror! You can also read this in conjunction with my guide on Value at Risk and other Key Risk Indicators below. http://tinyurl.com/ydvf3zh

Bull versus Bear Investing; versus Herding

The lifecycle (or holding period) of an investment held by a particular investor, often categorised as short, medium or long-term.

Let's get normal volatility out of the way first.. VaR-based toolkit.

Ok - a starting point - let's get normal volatility out of the way first.. This pack was written around end Q308 - post 16/8 but before the massive movement of Oct-Nov08. For those who support brownian motion or the geometric movement of returns then, I'm afraid to say, it's going to end bad..

What is the fuss with volatility.....

Re the movement of market returns - many believe they follow a geometric or exponential Brownian motion ('GBM') which is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion, also called a Wiener process. It is used particularly in the field of option pricing because a quantity that follows a GBM may take any positive value, and only the fractional changes of the random variate are significant ('deltas').

http://en.wikipedia.org/wiki/Geometric_Brownian_motion


So in practice 'brownian motion' assumes a strong tendency to trend - it says that returns won't jump from day 1 to day 2 but move up and down in fairly predictable increments.. the returns of the previous days have an impact on the subsequent day - they are not unique. This estimation of how prices move is the underlying principal for the future pricing of derivatives contracts such as options.. i.e. E.g. to buy a contract, at one price, to buy or sell the underlying asset at a future date at a future price... this is usually referred to as the 'Black-Scholes formula' or the much much earlier Bronzin model (1908). This ties up with the old-age 'law of big numbers' (or law of averages) - where returns follow a pattern around a mean and that the volatility around that mean diminishes over time.. Where those returns are then assumed to form a normal distribution (or bell curve) then the 'GBM' is symmetrical to the mean of those returns. BUT what if we do not believe upside and downside returns will be similiar?.
A LOT of analysis has been run since to dispel this view such as many variations of the the Noble winner Robert Engle's ARCH approach in 2003 ('heteroskedasticity'.. or the analysis of different dispersions/volatilities), countless variations thereof, stochastic models (see below*), extreme loss analysis, stress testing, scenario analysis and so on - it keeps the Math boys busy shall we say...

*Stochastic models: treat the underlying security's volatility as a random process, governed by variables such as the price level of the underlying, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Somtimes I use Markov chain as the easiest way to visualise and understand a random process: usually it's illustrated by the cat and the mouse:

Suppose you have a timer and a row of five adjacent boxes, with a cat in the first box and a mouse in the fifth one at time zero. The cat and the mouse both jump to a random adjacent box when the timer advances. E.g. if the cat is in the second box and the mouse in the fourth one, the probability is one fourth that the cat will be in the first box and the mouse in the fifth after the timer advances. When the timer advances again, the probability is one that the cat is in box two and the mouse in box four. The cat eats the mouse if both end up in the same box, at which time the game ends. The random variable K gives the number of time steps the mouse stays in the game..

This Markov chain then has 5 states:

State 1: cat in the first box, mouse in the third box: (1, 3)
State 2: cat in the first box, mouse in the fifth box: (1, 5)
State 3: cat in the second box, mouse in the fourth box: (2, 4)
State 4: cat in the third box, mouse in the fifth box: (3, 5)
State 5: the cat ate the mouse and the game ended: F.

To show this for a fairly infinite number of price movements is somewhat less achievable but nonetheless that's what the clever bods have done..

Otherwise most of probability, I admit, is above my head unless it descends into some sort of practical application - BUT I get the sub-plot.. stop trying to predict future patterns from regressing past performance... show me the track record of a model (after it has been created) and I'll be one step closer to being converted.. I'll touch on stress testing, extreme analysis ('extremistan') and scenarios another day..

"The Black–Scholes model disagrees with reality in a number of ways, some significant. It is widely employed as a useful approximation, but proper application requires understanding its limitations -blindly following the model exposes the user to unexpected risk. In short, while in the Black–Scholes model one can perfectly hedge options by simply Delta hedging, in practice there are many other sources of risk." Wikpedia

http://en.wikipedia.org/wiki/Black%E2%80%93Scholes





Active-Passive Investing Debate

Performance Patterns: **This deck is based on some work-based research so apologies for the confusing arguments - as a consequence the 'story' in the slides is a little muddy so I will re-jig this in the New Year to make my points clearer.** Passive-active purchase drivers in the UK are less differentiated/defined than perhaps elsewhere; the basic rules apply: What I did find was that there were interesting herding flows preceding, into and of the credit crunch. These were large asset-class movements: something which active managers would have little control of unless they ran absolute return type startegies. What my analysis showed is that an investor could manage a passive portfolio tactically to take advantage of large herding patterns. This involves risk, access to the right data, practice and above all discipline but I hope it will be a journey we can share!!

Lessons for 2010 - REIT Funds

Noting the events around 2005-2008 make for interesting considerations when thinking about buying REIT Funds in 2010..

The UK Investor - The Surprise Factor

The maps in the presentation (below) really help illustrate the suprise factor of the credit crunch.. little of the previous patterns would prepare the UK investor for what was about to come. The flows show that investors did not recognise the risks inherent in 2006-2008. This is because the industry uses conventional fund metrics, which were at best outputs not guides..!

The UK Investor - IMA 'Map' 2002-2008

Jon Beckett, ASCI - Past Projects (2003-2008)

I have been involved in the IFA and investment market since 1998, covering a broad range of roles. I have engaged a number of industry bodies over the years, to be a voice for change, to reform our industry and make it trusted and respected. None of the projects shown should be related to Franklin Templeton either: explicit, inferred or otherwise. I attach some of my past projects from 2004-2008.. Rgds JB