Forecasting - 10 Methods

By Gunter Meissner

In physics, some phenomena, such as the movement of the stars or the movement of time, can be forecast with 100% certainty. The future of economic and financial variables, such as interest rates or stock prices, however, is uncertain. But we can forecast them with a certain probability. That is what this book does.
We discuss 10 methods, from simple methods such as fundamental and technical analysis, to established statistical methods such as linear and non-linear regression function extrapolation. We also discuss the latest developments such as stochastic processes, extreme value theory, and forecasting with AI. So we hope the book is valuable to a wide audience.
This book comes with 14 Excel spreadsheets and 10 Videos. We also display 7 Python codes, which can be run online at repl.it.

• Language: English
• Publisher: BookBaby
• Release date: Sep 15, 2020
• ISBN: 9781098333874

Book preview

Index

Fear is a reaction, courage is a decision Winston Churchill

INTRODUCTION: FUTURE UNCERTAINTY AND HUMAN BEHAVIOR

In this chapter we discuss the response of human beings to uncertainty. We analyse the risk-aversion of humans with respect to uncertainty, whether risk-aversion is rational, and whether it can be exploited.

Forecasting gone wrong

Let’s start this chapter with some forecasting quotes:

God himself could not sink this ship Captain Edward Smith of the Titanic

Stock markets have reached what looks like a permanently high plateau. Irving Fisher, New York Times in 1929, just before the stock market crash of 90%

I just have a hunch that Stalin is not that kind of [evil] man FDR on Stalin

Bear Stearns is fine. Do not take your money out! Jim Kramer from CNBC in 2008, just before Bear Stearns crashed from $62 to $2.

Hillary Clinton has an 85% chance to win New York Times on November 8, 2016, the day of the election.

What is the take-away from these forecasts or unforeseen events such as the 1906 San Francisco earthquake, the Japanese attack on Pearl Harbour 1941, the 9/11 Terrorist attack in 2001, or the Covid19 shock in 2020? It is that extreme events have a non-zero probability. So we should always be aware of extreme tail events¹ and try to forecast them to avoid their detrimental impacts. We will quantify these extreme tail events in chapter 9, Extreme Value Theory.

Nothing is certain but death and taxes Benjamin Franklin

Is all Future Uncertain?

Well, almost. Exceptions are the movement of the stars and planets in the short term. The death of stars, such as our sun is also certain. Our sun will run out of hydrogen and turn into a red giant, burning the planets in our solar system. Don’t worry though, this will happen in about 5 billion years, so we have some time to tackle the problem. The universe’s expansion, which is accelerating, will also continue for the foreseeable future.

However, most economic variables such as GDP growth rate, unemployment, inflation, interest rates or trade balance are uncertain. The same logic applies to financial variables such as stocks, bonds, exchange rates, commodities, or option and future prices. In this book we will suggest 10 methods to forecast, i.e. find probabilities for the future state of economic and financial variables.

How do Human Beings react to Future Uncertainty?

Humans beings buy insurance to reduce unforeseeable future harm. This is why most people have health insurance for their family and themselves. The principle of insurance is that an individual is protected by the community of insurance buyers. For example, if a person gets very sick, the health insurance will cover the cost from the premiums of the other insurance buyers.

There is a big discussion in the US on whether health insurance is a privilege or a human right. In Europe this discussion does not exist, since most Europeans believe health insurance should be available to everyone.

Should insurance be mandatory? If a person can harm another person with his or her action, then yes. A good example is car insurance. If an individual hurts a person or their property with his/her car, the individual may not be able to cover the cost, but the insurance is typically able to. Therefore, car insurance is mandatory.

Should homeowner’s insurance be mandatory? If a person lives in a high-rise, then yes. He or she can possibly burn down the whole building and harm others. Which brings us back to the question of health insurance. Should it be mandatory? Insurance only works if there are many insurance buyers who do not actually use the insurance. So young people who often do not get very sick, should also buy health insurance. That is why Obamacare has a penalty for not buying health insurance.²

Another interesting question is whether buying insurance is a zero-sum game. In a zero-sum game, what person A gains, person B loses, as in a stock trade. If A sells the Apple stock to B at $300, and the Apple stock goes to $290, A gains $10 and B loses the same amount of $10 (assuming no commissions and transaction cost). So is buying insurance a zero-sum game? The answer is, typically no: If a person has health insurance and never uses it, it does give peace of mind. So the person does benefit, just as the insurance seller does monetarily from selling the insurance. The same non-zero game property applies to other insurances, such as life insurance or homeowners insurance.

How do Human Beings deal with Risk?

Although in finance every risk is an opportunity, most human beings don’t like risk. We can define human risk-aversion as

A risk-averse person prefers an outcome with certainty over the same outcome with uncertainty

An example would be: Option 1: A person is offered $50,000 with certainty. Option 2: The person can gamble with a coin: He gets $100,000 for Heads and $0 for Tails. Most humans would take the $50,000 with certainty since they are risk-averse. A risk-neutral person would be indifferent between option 1 and 2. A risk-loving person would prefer option 2.

The degree of risk-aversion can be seen in Table 1. The answers are from students.

Table 1: Different Degrees of Risk-Aversion

In Table 1, 90% of students were risk-averse. 5% of students were highly risk-averse, preferring $20,000 with certainty over gambling with an expected outcome of $50,000. 10% of students reported being indifferent to taking the $50,000 with certainty and gambling for it (not displayed in Table 1). They are considered risk-neutral. A risk-loving person would gamble for the $50,000 even if he or she is offered an amount higher than $50,000 with certainty. In my many years of playing this game, about 1% of students were risk-loving.

Graphically, risk-aversion is displayed in Figures 1:

Figure 1: Risk-Aversion: The utility of $50,000 with certainty is higher than the utility of $50,000 with uncertainty i.e. U (Gamble)

What factors determine the degree of a person’s risk-aversion? One factor is genetical. Some humans are just more risk-averse than others. Another factor is wealth. As the saying goes: Money matters when you don’t have it. So if a person is in financial need such as a mortgagor having to make mortgage payments or a student who has student debt, risk-aversion is typically higher. Another factor can be age. Risk-aversion with respect to age may be a u-shaped function: A student in her early 20s with little or no income may be quite financially risk-averse. A person in her 30s, 40s, and 50s may have a higher financial risk-tolerance, i.e. have a lower risk-aversion. With older age, typically risk-aversion increases again.

Risk-Aversion is everywhere in Finance

In Table 1 and Figures 1 we displayed risk-aversion. Risk-aversion can also be found in many areas in financial reality. One of the first to point out risk-aversion in financial markets was Edward Altman in 1989: A bond-yield spread is the difference between a risky bond yield and a risk-free Treasury bond yield. This bond yield spread is a measure of the default probability of a bond in reality³. Comparing the bond yield spread to historical default probabilities of bonds, we find that the bond yield spread is significantly higher than historical default probabilities as seen in Table 2:

Table 2: Low historical bond default probabilities compared to bond yield spreads (which are bond price implied default probabilities).

The take-away from Table 2 is that bond prices in the market overestimate bond default probabilities. For a Baa rated bond, the bond yield spread is about 5 times higher than the historical default probability! This means that investors are risk-averse, i.e. bond prices are too low compared to their historical default probabilities. On an absolute level this is especially true of junk bonds (bonds with a rating of Ba, B, and Caa) as seen in Table 2.

Risk-aversion is also a property of the Nobel prize awarded Capital Asset Pricing Model (CAPM), developed mainly by William Sharpe, Harry Markowitz, and Merton Miller. The core idea is that investors require a higher return for higher risk. This is displayed in Figures 2.

Figure 2: Expected Return as a function of Risk

The risk in Figures 2 is measured with the famous β=Covariance(P,M)Variance(M), where P is the return of the portfolio in question and M is the market return, for example the return of the S&P 500. For a proof that the regression coefficient β=Covariance(P,M)Variance(M) see www.dersoft.com/betaproof.docx. The key result of Figures 2 is that investors require a higher expected return for higher risk, i.e. are risk-averse. In case an investor does not want to take any risk (β=0), he can buy Treasury bonds, which have a low return.

We also find risk-aversion in the option market: Implied volatility, the only free variable of an option trader to determine an option price, is typically higher than historical volatility. This means that options are overvalued. Put options, when the underlying is owned (called ‘married puts’), act as an insurance against decreasing stock prices. Hence investors are overvaluing options, i.e. they are paying a risk-premium for the put insurance, which constitutes risk-aversion.

A further, more complex example of risk-aversion, is in the variance swap market. A variance swap allows an investor to trade his view on the future variance of an asset. Going long variance means receiving realized variance and paying a fixed strike, i.e. the payoff is N(σ²realized - σ²strike), where N is the notional amount. The strike of variance swaps is often higher than historically justified, hence the variance swap market is overestimating variance, which is a measure of risk. Thus we have risk-aversion in the variance swap market.

A last example of risk-aversion is in the dispersion market. Dispersion trading allows an investor to take a position in the future correlation between the assets in an index. If a recession is forecasted, a trader should go short dispersion, i.e. buy options on the whole index and sell options on individual index components. This is beneficial since correlations often increase in a recession and the whole index declines sharply. Therefore, the options on the index are expected to increase more than the options on individual index components. In the dispersion market, often IOIV, index option implied volatility is higher than MIV, Markowitz implied volatility, which is the volatility of the index components. Hence traders in the dispersion market overestimate the whole index declining, which constitutes risk-aversion.

Markets can stay longer irrational than you can remain solvent John Maynard Keynes

Is being risk-averse irrational?

Well, following the law of large numbers⁴, in the long run, yes: Let’s assume option 1 is $40,000 with certainty and option 2 is flipping a coin, receiving $0 for Heads and $100,000 for Tails. If the coin is flipped 1 million times and the results are averaged, the outcome will be close to $50,000. Therefore it would be irrational to take the $40,000 with certainty. However, the less the coin is flipped, the more rational it is to take the $40,000. If the coin is flipped 10 times, the gambler may be unlucky, and 8 times Heads appears, so the outcome would be $20,000. For a one-time flip, naturally, there is a 50% chance of a zero outcome.

The same logic applies to financial reality. In the long run, market distortions due to investor risk-aversion can be exploited. In the long run it is more reasonable to take risks, e.g. to invest in stocks rather than bonds, since the annual return of US stocks since 1920 was 7.9% (including reinvested dividends) whereas the annual return of the 10-year Treasury bond was 3.2%. However, in the short run, there may be a severe recession. In the 1929 to 1932 Great Depression, the Dow Jones Industrial Average declined by about 90%, in the 2007 to 2009 Great Recession, the Dow declined 54.1%, and during the Coronavirus recession in 2020 the Dow declined 37.09%. Hence a reliable forecast of a recession increases the rationality to be risk-averse. So we see