Financial Markets - Risk Management

It is true to say that if you thought you were incorrect about a football team or the FTSE, you wouldn't make the wager. Obviously there will be times you are wrong, and so lose your money. The solution to making a gain on balance is to use clever risk management, so avoiding a loss and increasing profit.

Stop losses are frequently proffered as the first line of defence in risk management - presumably ensuring that a trader is profitable by guaranteeing losses don't eat into his capital. However it's never that simple. In a vacuum, a stop loss method is at best a neutral strategy but in practise, due to costs, a slightly negative one. There is no free money to be earned in the market and a robotic stop loss system can't tot up to a trader's returns unless he is already trading so badly that he is doomed anyway.

Doing the random walk. Oi!
What happens next is underpinned by the idea that markets are usually highly random. Randomness isn't a word many traders or investors like to hear - how does a trader forecast the market when it's random? Nevertheless, a look at stock price histories will show bell curves of distribution again and again. Bell curves are the proof of randomness and plot the spread of results created by a process. The bell curve stands for a statistical evenness suggesting that the process is generating random outcomes, comparable to dice being rolled on a tabletop.

A case in point, obtained from my records, is a graph of five years' worth of Dow moves between the commencement of business and the previous night's close. This bell-curve allocation is the footmark by which physicists call 'the random walk'. To view this graph, click the 'How To' button.

In spite of this randomness, by reading and taking advantage of short-term trends, it is still conceivable to make a profit in line with the risks you are taking. If it wasn't, you could invest your money in the bank and wait for retirement. The key to acquiring returns while avoiding disaster is risk management. Averting disaster sounds like a good idea, yet many traders simply don't. This frequently occurs because they either don't understand the risks or the full, potential ramifications of taking them.

At this stage I'd like to introduce the martingale. This is a system that includes increasing stake size as a run of losses extends. Typically, the martingale comes into play with gambling games like blackjack or roulette, where a stake is doubled after every sequential loss. When a win is produced, the player gets back his losses and earns a 'one-unit' win; the stake size is then reset. Simply, with infinite capital you'll consistently end up winning in the end.

The martingale and its countless permutations are popular systems for trading. But, the model is flawed as, in fact, you are liable to run out of money before your luck turns. Bad luck simply occurs with greater regularity than the capital required to fund the operation. I've actually witnessed red come up 23 times in succession on a roulette table. If the martingale system had been used, it would have cost me £4 million to win back my £1 - and even if I had £4 million, the table limit would beat me.

Another classic example of the dangers of misunderstanding risk management is the early 20th Century phenomenon of the 'bucket shop'.

These consisted of stock market day trading systems run by unlicensed trading establishments. The trading guidelines were simple. You could, for example, buy a £100 share on margin for £2 (50 times leverage). This £2 also functioned as a stop loss. If the share went down £2, the position was closed and you lost your margin money. If the share got to £110 or higher, you would make the amount by which the price had surpassed £100 (£14 if it reached £114, £50 for £150, etc).

An established downside with an infinite upside looks like too good an offer to refuse, but volatility and probability are formidable enemies in this set-up. Even if the odds of this trade are marginally in your favour, on a random basis, a price will at some point go under £100 around nine times out of ten. So with an entire £2 margin, you could get stopped out quite easily. If a price has an average daily span of four points even in a sideways trend, you are going to be closed out every time. It takes quite a good leap for a stock not to hit £98 at some point in the future of the proceedings. One go and you're out. This is the general rule of gambler's ruin in microcosm, and it is essential to avoid it.

The view from Kelly's eye
Anyway, if stop losses on their own are not the answer, what is? Think of a roulette table and imagine the wheel has 35 reds on it and one black, yet the payout is still even money. On this table you are able to make lots of money very quickly indeed, yet we can still lose everything. If you have 100 £1 chips and play £1 at a time we'll make £1, 35 times out of 36. That's nice but hardly optimal - after all, we could get very rich very quickly at this table. Place £2 down and we would clearly make twice as much per go. We could place £4 or £10 down at each turn and increase our profit each time. Nevertheless, the greater your stake, the greater the probability of a run of bad luck taking all your money.

So, if we consider that this uncommonly gambler-friendly wheel will only be open for one night and we only have £100 to play, how do we get the most favourable returns? We can be convinced that if we do find a wrinkle in the market it won't last forever, so extracting value will always be against the clock. The question for us is how to make as much as possible that evening.

The answer is not to put down the whole of your money on the red each time as despite the fact that the chance of black coming up is low, it will come up. If you did this you'd lose all your money and experience gambler's ruin. So in between £1 and £100 a go, there's an optimal stake threshold, which increases your return but avoids gambler's ruin.

In equities, this stake limit is frequently said to be between 2.5% to 5% of your investment capital.In options trading it's recommended that a trader needs capital of three times his maximum losing streak. The losing streak distributed by the capital lost would therefore dictate the position size.

Mathematically, the principle - known as Kelly's Optimisation Model - is a lot more exact. This model is frequently used in gambling but is just as applicable to investment. It believes the size of a positive outcome is the same as for a negative outcome and as such is a useful outlet for stop losses.

If the probability of the trade becoming good is 52.5% (5.25 times out of 10) then the Kelly model says you should put: (2x0.525)-1 of your capital on the trade. Consider 1.05-1 of your investment or 5%. If your odds were 90% then you should bet: (0.9x2)-1, which is 1.8-1 or 80% of your capital.

While it is appealing to know exactly where results are optimal, it's crucial to realise that if you stake more than the sum given by this equation, you are assured to be affected by gambler's ruin. It might take time, but it's a mathematical certainty.

If you considered trying Kelly's Optimisation, the size of your positions would be right on the make-or-break line. This is rather a torrid place, so many gamblers simply back 50% of this amount, on the basis that they will still make plenty of money but avoid the ulcer. In the example of our odd roulette wheel, it only takes an hour or so to own the casino whether you back a half or a whole of the amount.

Any portfolio in a storm
Here, we've just evaded the disaster of compound events. The similar technique to this is portfolio management, where resources are dispersed in such a way that they are engaged in risk yet protected from what is known as 'unsystemic risk'. An instance of unsystemic risk would be that our wonky roulette table would be brought to the attention of the casino management's attention and we finish up wearing a concrete overcoat. Portfolio management defends against us suffering gambler's ruin caused by a single disaster.

While Kelly's optimisation administers the allocation of resources for a single position, portfolio management depicts the type of simultaneous positions to carry. Using diversification, more capital can be safely disposed and therefore a better return made.

Portfolio theory deliberates that a market has a systemic rate of return. This ratio is, on average, proportional to the risk involved with the instrument invested in. For instance, return on government bonds will be small as the risk is low; corporate bonds are riskier, so returns will be higher. As risk levels develop for any instrument, so does the chance of a big loss. The problem is choosing the risky stock that won't crash.

Portfolio theory's answer to this is to boy a bundle, thus capturing the average result, as winners will counterbalance losers. Advocates of the random walk affirm that this is the best you can do in any event as markets, like the weather, are impossible to predict.

Not including all your eggs in one basket is not the most revolutionary of maxims, but taking into consideration the volatility - and thus, risk - of an asset, the more varieties of them that are held, the more confident your money is of growing at the 'systemic return'. In the case of equities, this is believed to be 30 or more stocks in a portfolio.

You could, for example, choose a portfolio of tech stocks. By doing this, you would obtain the returns of the tech sector, without making yourself exposed to wipe-out on a single stock. Alternatively, you could take returns on an entire market, or perhaps the returns of a collection of markets, or even a broad spread of different asset types. Portfolio theory allows you to slice and dice the risk return potential of all kinds of markets.

While developing a portfolio might feel like removing the thrill of risk, it can be used to boost returns, by providing a structure for holding extremely risky investments. To seize these returns, the portfolio must be wider. That way, some big winners will cancel the large proportion of losses. This is not free money; you are being compensated for taking risk and providing liquidity.