This is the first in a series of Quantdary articles that will seek to acquaint the reader with investment management, particularly in regards to protection from financial abuse.
Imagine being able to borrow from your wealthier future self to help finance the deficits your current self faces. Or imagine being able to transport goods or wealth beyond your current level of consumption to your future self. The wonderful news is that this is not some futuristic technology ripped off science fiction, but an ancient art known as investment. This idea has so fascinated scholars that it has become a key component in disciplines like economics and finance, formalised in a notion called “inter-temporal choice optimisation.” Most people in such fields have an intuitive understanding and appreciation of the importance of investment. Firm managers typically engage in capital budgeting to help decide the investment choices of their firms, whereas investors seek the help of financial advisors to help allocate their savings to different sources of investments.
Yet the investment process is not always a well-oiled machine. In fact, the myriad of agents operating it sometimes have off-setting goals, to the extent that the benefits from being able to transfer wealth across time is offset by attempts to “transfer” wealth from one agent to the other. It is readily conceded that it is unrealistic to expect all investors to possess an understanding of all the technical details involved in making capital budgeting decisions or how to price a security that they are interested in investing. However, knowing how to ask the right questions and understanding the building blocks of these processes can go a long way.
The basic principles behind investment management are simple, but implementing them in practice prove to be more challenging. The complexity of asset prices and their intricate relationships have fueled the growth of industries that hire specialists to deal with the increasingly technical nature of investment. Those who tried to navigate the “inner baseball” of finance can attest to the overwhelming amount of asset pricing models and intimidating equations that easily crashes the average computer from its demand on computational power. Such complexities have led to specialisation, and while the nature of specialisation has allowed humanity to accrue economic gains, it has also introduced an opaque layer to the non-specialists. Consider the attitude that prevailed before the Great Financial Crisis of 07/08, where a false sense (in retrospect) of security on financial securities lay under the veneer of complex arrangements and pricing formulas. Since the GFC of 07/08, the attitude has shifted to an equally extreme and unhealthy “black-box” aversion, characterised by an unwillingness to explore products that appear too complicated.
The swing in attitude towards the extremes tells two tales of tragedy. The complacent attitude in before GFC 07/08 has exposed investors to risk that are ill-suited for them–indeed, the legal repercussions that some sellers of these securities are still tangled in today are evidence of the complexity of their abuses and intentional disinformation. On the other hand, the “black-box” aversion developed by investors who realised how vulnerable they were when complacent have also resulted in a loss in welfare. Financial engineering is a technical field that combines the payoffs of a combination of securities and derivatives to help investors mitigate risks that they are not willing to take. A complete rejection of some of these complex products would reduce the means of mitigating unique risks faced by some investors of firms. In order to progress to a middle ground between these two tragic views, it is thus important to understand the basic building blocks of pricing models. By knowing enough to ask the right questions, investors are able to look beyond the façade of technicalities and complex arrangement to assess the suitability of a product, or decide on which financial advisor to hire. Moreover, a basic understanding of how securities are priced would act as a mental discipline against a “black-box” syndrome, so that the right product that helps mitigate a risk source an investor is averse too is not rejected without consideration.
A natural starting point then, would be to ponder on the question of how securities are priced i.e. how should investments be priced? The approach is actually quite simple, and we can think of the interest rate as a bridge that links the present to the future. By choosing to consume today, we are also simultaneously choosing to forgo the opportunity that today’s consumption is not saved, which will not translate to a higher consumption level tomorrow.
So suppose you have two coconuts, which you could either consume today, or “invest” by planting it so that you get 3 coconuts tomorrow. The return of your coconut investment is thus 50% . (Return is calculated as final wealth – initial wealth divided by initial wealth). There’s still a lingering issue however: while it is true that if I am patient and invest the two coconuts today, I will get a 50% return and thus enjoy 3 coconuts tomorrow, but how much are 3 coconuts tomorrow worth today for me? To help make sense of that, you discount the 3 coconuts you get from the investment at a rate of 50% (the price of investment), giving you two. So since 3 coconuts tomorrow is worth 2 coconuts today, you are quite indifferent between consuming and investing. Of course we can relax this parable a bit more. For instance, your neighbor Christopher Walken might have given you some pineapples today, and since you have too much food today, you’ll decide to eat the pineapple today and plant the coconuts instead. That is essentially shifting today’s surplus wealth to your future self for consumption. These are interesting extensions, but let’s confine our attention to interest rates for now. The approach of analysis used in this parable is what is known as the present value of an investment/security, and it is an essential concept in finance.
An important caveat to note of the above parable is that the discount rates used need not always be the return or the expected returns. Bond prices for example, are determined by interest rates, and the holding period returns of bonds are not necessarily the yields used to discount the bonds.
Moreover, there are a lot of interest rates to be used to priced securities. In fact, there are varying interest rates for different time horizon and different agents, so a 2 year interest rate is different from a 1 year interest rate, and the government borrows at a different rate than say, Scotiabank. Yet despite the details, the valuation of security works pretty much the same way. You consider the payoffs (which need not be certain) you receive from a security at each point in the future, and discount it with the appropriate interest rate to translate to how much it is worth today.
Hence the best way to think about discount rates is that they are essentially compensation for patience and the risks being assumed by an investor today. As a result of being patient and bearing risks, you get to pay less than, say, $100 to receive $100 in 6 months. The price you pay today is simply the present value of the security after discounting to compensate you for patience and risk-taking.
Finance may be portrayed as a field of windfall fortunes, with money coming out of thin air. We can all share our encounter with “that guy”, you know, the blokes who would “explainabrag” (a brag disguised as an explanation) about how their huge returns from a particular investment has made them richer. While there were some anecdotes for the explainabraggers, a healthier view is to not regard investments as a magic beanstalk. At its core, it is a way of shifting consumption, and the interest rates you receive (pay) is simply a result of compensation for patience (impatience), the risks you bear (avoid) and some market anomalies that stem from behaviourial biases. What matters is how your investment management strategies cater to your risk profile and needs, and how to avoid value transfers to unscrupulous parties.