There are risks in every investment. Along with the risks, there is also an expected return. The risks of an investment could mean the possibility of losing some of the capital otherwise known as Value at Risk (VAR). Risks can also be referred to as the uncertainty that the expected return (Re) is not achieved or the actual return (Ra) is lower than Re.
Investment is a calculated bet
In view of the uncertainty involved, whenever an investment is made, the investment can be considered as a bet. Although the term “bet” sounds very much like gambling, but unlike gambling, investment is not entirely based on pure luck. Even in gambling, be it casino or number forecasting games, there is the probability of outcome and prize payout. Simple probability computations based on payout rates show that the final payout is always less than the betted amount. As such, when wagering in these games, the returns are always negative.
In the case of investment, the bet refers more towards the uncertainty of the return, even though the risk is a calculated one after having taken into consideration the potential loss as well as the potential return that can be derived from such a bet.
When we refer to an investment as a bet, we simply mean that an investment has a risk of losing money and that is a fact. Each investment should be seen separately and independently. An array of investments makes a portfolio of calculated bets.
Mental calculation
Many investors use mental calculations to decide whether an investment is worth considering or not. Experienced investors will use his or her past knowledge to make a decision. Based on this valuable skill, a quick response can be made without performing much computation. As such, experience is very important, and it helps a lot in making quick decisions — especially during such periods of volatility.
However, for those who have limited experience, additional homework is needed to calculate and determine the return and risk trade-off. In many cases, the expected returns and probabilities cannot be determined easily, however, systematic procedures in making return and risk computations can still provide the lead.
High and low probability
The return from an investment can be simplified as follows:
Expected Return = profit from a bet x probability of occurrence; or
Re = Pi x pi
Under normal circumstances, a high probability (or high certainty), comes with low profit (a good example is fixed deposits in a bank). Similarly, a low probability event (or lower certainty) is most likely to be compensated with a high possible profit (a typical example is share investment). It is very rare, or unheard of, to have an investment giving good profit and also high probability (unless it is a Ponzi scheme). Such “opportunity” calls for closer scrutiny. Sensible investors will avoid low possible return of an investment, which has a low probability of occurrence.
Two-scenario probability
In most events, there are two scenarios — pno if the event does not happen, and pyes if the event happens.
Re = Pyes x pyes + Pno x pno, where Pyes is the profit if the expected event happens and Pno is the profit if the expected event does not happen.
A simple example is a guaranteed fund whereby 90% of the fund is locked into a zero-coupon bond to provide the capital guarantee and the balance 10% of the fund is used to bet on an idea. If the idea does not work, Pno = 0. Assuming the idea can yield a return of 80%, Pyes = 80%, and the fund manager betting on the idea has a 60% probability of hitting it right, then pyes = 60%, and correspondingly the chance of betting wrongly is 40% (pno = 40%.)
Since the bond will mature to give its original capital value, the profit will entirely come from the investment portion whereby the expected return is:
Re = Pyes x pyes + Pno x pno
Re = 80% x 0.6 + 0% x 0.4
= 48%
As only 10% of the fund is invested in the bet, the eventually return is 48% x 10% = 4.8% yield to investors.
Using probabilityin technical trades
Many people like to use technical tools to time the market. Technical indicators rely on past price and volume data to provide certain signals, and some of these signals are used as buy or sell indicators. Technical chartists know that there is no guarantee that charts can be right all the time. The technicians know that charts can also be wrong, as there could be other events that caused the price to move against the predictions. Some will include emergence of new buyers or new sellers, which have not been picked up by previous trades.
For illustration, assuming the support-resistance levels are derived from the historical price pattern of a stock, say in the case of Tanjong plc. The price of Tanjong hit a low of RM12.20 two times in July (A, B), then it tested the level again in August (C) (see chart).
The probability that support C could be broken was lower than 50%, maybe say 35%. The price subsequently recovered to RM13.50, before heading towards the RM12.20 support zone again. Based on the past three attempts at RM12.20 there seemed to be some buyers (some may call them “invisible hands”) willing to buy or support the price at RM12.20. As such, the probability that Tanjong would go below RM12.20 support level in September (D) was low, say 25%. Therefore, it was a good entry level around D.
After rebounding from D, the price tested RM12.20 again at E in October. Again, the chances of support E being broken could be remote say 15%, but this time the support was unfortunately broken and a sell signal was obvious. The share price fell nearly 20% after the support was broken.
This is just an illustration. Confidence level can be incorporated to determine the strength of the technical signal, and the accuracy of the signal is used to determine how a bet can be made. If the confidence level is high, then a larger position can be placed for the bet. On the other hand, if we are not too certain about a technical signal, the bet could be 50/50 right or wrong — or marginally, 55/45 right or wrong, which may not be very profitable.
What we want is to select a bet where the downside is low if we are wrong, and reap a good profit if we are right. Coming back to Tanjong’s case, the maximum upside purely based on the chart is only RM1.30 (RM13.50 minus RM12.20) or 10%. The downside is unknown from the chart’s point of view. To minimise risk, a cut loss strategy must be put in place to limit the loss, say a maximum of RM0.20 or 2%, by squaring off the position at RM12.00 if the price deteriorates beyond RM12.20.
At point D,
Re = Pyes x pyes + Pno x pno
= (1.30) x 0.75 + (-0.20) x 0.25
= 0.975 - 0.05
= 0.925
Each trade at point D can probably make RM0.925 or 7.6%. Using this method, one can estimate where we stand if we take the bet and how the risk/return will trade off.
At point E,
Re = Pyes x pyes + Pno x pno
= (1.30) x 0.85 + (-0.20) x 0.15
= 1.105 - 0.03
= 1.075
Point E was supposed to be a more profitable entry level, with a potential profit of RM1.075 or 8.8% per trade. Unfortunately, the market came down and a cut loss strategy must be immediately put in place.
Using probability in news
Many people also like to trade on news. Assuming in a speculation, rumours that a company will get a contract caused the share price to go up from RM5.00 to RM5.40. If success in getting the contract will add RM0.80 to the bottom line of the company, then the share price may eventually move to RM5.80 — ie, a further upside of RM0.40 per share. If the news is false or the company is not able to get the contact, then the share price should fall back to its original position of RM5.00.
Assuming that the chance the company will secure the contract is 70%, we can then compute the expected return from purchasing the stock at RM5.40 as follows :
Re = Pyes x pyes + Pno x pno
= (0.40) x 0.7 + (-0.40) x 0.3
= 0.28 - 0.12
= 0.16
The expected profit Re from the above bet is RM0.16 or 3%. If the return is very small, a review is needed to re-assess the probability pyes to determine whether the 70% likelihood is realistic or not.
Using probability in takeover
In a voluntary general offer (GO) to take over a listed company, the share price would go up to a level several percentage points short of the GO price. Assuming the price surges from RM3.00 prior to the GO announcement to RM3.68, and the GO price is set at RM4.00. The potential upside if the deal is completed is RM0.32 per share.
The reason why there is still an 8% discount from the GO price is the uncertainty that the GO may be aborted for any reason. Some of the possibilities include difficulty in raising the needed funds, inability to secure more than 50% of the votes to make the GO unconditional, approval of the authorities, etc.
Assuming in this GO deal that the probability the deal can be completed is 90%, perhaps the acquirer is a government-linked agency which is more determined to take the company private. The expected return Re from investing in the stock while waiting for the completion of the GO is:
Re = Pyes x pyes + Pno x pno
= (0.32) x 0.9 + (-0.68) x 0.1
= 0.288 - 0.068 = 0.22
The GO will probably provide a return of RM0.22 per share or 6% return, which is attractive for the high degree of certainty.
Complex scenario
The above examples are illustrations whereby the deals are either on or off, true or false. In real life, there are many deals which are much more complicated. Some could be a three-stage scenario, whereby the probability is up, sideways or down.
In most cases, the probability is not so discrete. It is in a continuous form represented by a normal distribution. The outcome of such a bet is the expected return Re and the standard deviation of return, o. A big o means that the risk is high and the normal distribution has fat tails from the mean. A small o means the risk is lower and the normal distribution is concentrated around Re.
Examples of non-discrete events are the probability that a share price will go up 20% in three months, the probability that the gold price will exceed its recent high of US$1,000 (RM3,620) per oz, etc. Based on past volatility of the price, predictions can be made on such probabilities, and they are widely used by investment banks to design various structured products.
Hedge funds use probability
The probability concept in investment is widely used in the hedge fund world. Each investment idea is viewed individually in terms of risk and return. The concept is rationale and highly objective. The expected return of each idea is computed, and a simple comparison will allow the investment manager to determine which idea is a better bet. Since there are likely to be many investment ideas coming in at any moment, the computer is needed to filter through the huge amount of data.
By putting in the estimated expected return and corresponding probability into the computer, better bets will be selected by the computer for the investment manager’s consideration. If the computer programme is reliable and the input data on expected returns and probabilities are reasonable estimates, the selected investment ideas can be taken as buy or sell signals which can even be sent directly to the dealers for execution. This becomes the basis of programme trading.
Many hedge funds use quantitative methods to trade. In this way, hedge funds using quant methods can have many investment ideas or bets to choose from by churning the voluminous amount of data, which can range from economic data such as interest rates, inflation, imports and exports figures, loan growth, etc or technical data such as price and volume or even fundamental data such as earnings growth, analyst upgrade/downgrade ratio, market price earnings (P/E), market price/book ratio, earnings yield-interest rate differential, etc.
In short, investment is not a certain game. Hence, investors must develop a habit of using probability in each investment decision.
Ang has 20 years’ experience in research and investment. He is currently the chief investment officer of Phillip Capital Management Sdn Bhd.
This article appeared in The Edge Financial Daily, March 30, 2009.
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