This is the second in a series of Quantdary articles that will seek to demystify the investment management process to the general audience, and to arm investors with enough knowledge so as not to be led into investing in securities that are ill-suited for them. Much of the insights are derived from conversations with professors, portfolio managers and employees of financial institutions around Montreal. They are hopeful that the ongoing cultural shift in the business and investment management landscape will promote the welfare of investors.
The time value of money, encapsulated in the notion of present value, is one of the central tenets of Finance. As we saw in the previous article in the series, the present value expresses the value of some future future payoff in its worth today. We can thus see the indispensable role played by interest rates in interweaving the present with the future. Excesses (deficits) today can be financed through investing (borrowing) in the future, and this process is dictated by the level of discount rates.
A keen observer might note that while linking the present to the future is an important role of the financial sector to shift consumption patterns across time, this is not the sole function of a financial system. In fact, investors are often greeted with a myriad of investment products, ranging from chocolate-paying bonds to other forms of complex securities. Some of the complex instruments introduced by financial engineers are meant to cater to unique risk profiles of certain clients, and the pricing of complex securities have shed light on the limitations of relying solely on the present value approach for pricing. For instance, those unfamiliar with fixed-income pricing will not know how to value an interest rate swap. After all, if I had entered into an interest rate swap agreement last period, where I pay a fixed interest rate in exchange for receiving a “floating” (that is the interest rates that prevail in the market today), it is unclear how I should value the instrument right now, given that the interest rates conditions have changed.
Questions like these have led to the introduction of two popular frameworks to help in pricing securities: the no arbitrage framework and the first-principles based framework. Each framework introduces their own set of assumptions, with the latter tending to be more restrictive.
Before the two pricing frameworks are explored, it is first necessary to define precisely what we mean by “prices” and terms associated with it. In economics and finance, prices are always meant relatively, and never in an absolute sense. As a result, one rarely speaks of whether good A trading at X dollars and good B trading at Y dollars is cheap or expensive. These prices must be viewed in the context of an individual’s enjoyment of good A relative to good B. For instance, if the price of pineapple is twice that of watermelons, but an additional unit of pineapple gives me three times the enjoyment of a watermelon, then the price of pineapple is considered cheaper for me at this rate. I will then consume more pineapples until the last pineapple gives me twice the satisfaction as consuming an extra unit of watermelon. That level of consumption of pineapple and watermelon is thus the fruit bundle chosen by a utility-maximising individual.
Financial economists are quite often the butt of the joke in popular media. Many of us have heard about the story of two economists who were walking and found a 20 dollar bill lying on the floor. One of them tried to pick it up, before being chastised by the other economist, who challenged the existence of the 20 dollar bill. After all, the other economist proclaimed, if it were real someone would have already picked it up. The punchline of this joke is what is known as the “no free lunch” notion, and it is predicated on the law of one price.
The law of one price is often invoked to claim that the price of identical goods must trade at the same price, otherwise a profitable opportunity arises. After all, a 20 dollar bill can not lie on the floor for long, as someone will eventually pick it up. Similarly, Mars bars cannot be priced differently in Boston and Montreal. If there were price discrepancies after accounting for the exchange rates and costs, it will be worthwhile for a firm to import Mars bars from a the cheaper country and sell it at the country where Mars bars are more expensive. When a lot of firms do the same thing, they exert pressure on the prices of Mars bars in Boston and Montreal until they converge to the same price level, after adjusting for exchange rates and costs.
In the context of securities, a pair or set of securities that offer the same payoff and that are subject to the same discount rates should be trading at the same price. Otherwise, an arbitrage opportunity arises. Let us think of two examples. First, consider the stock price of IBM that is traded in Europe and the USA. Since the stocks are similar, that is, they pay the same dividends and are subject to the same discount rate (the cost of capital of IBM to be precise), the prices should be the same once the exchange rate is factored in. If there is a price discrepancy, an arbitrageur can profit by “shorting” (borrowing from the broker to sell at the market) the expensive IBM stock in one market, while simultaneously “going long” (buying) the cheaper IBM stock in the other market. The price discrepancy is thus the compensation to the arbitrageur for bringing prices in line. (Issues like market liquidity and possibly non-synchronous trading, i.e. price differences due to different trading hours are abstracted for the sake of exposition).
For the next example, consider the interest rate swap example presented in the beginning of this article. The instrument may appear difficult to price, but the no arbitrage framework allows us to simplify the problem and gives us the right answer. Since the interest rate swap mentioned is exactly similar to going short on a fixed rate bond and going long on a floating bond, we thus subtract the value of a fixed rate bond from that of a floating rate bond to give us the market value of the interest rate swap. If the interest swap were not priced at the same value as the method suggests, we can replicate the interest rate swap with a floating rate bond and a fixed rate bond, and enter into an offsetting position on the interest rate swaps such that the positions perfectly cancel each other out. The positive value that remains then, is the arbitrage profit.
While the no arbitrage framework have provided a powerful and simple framework for asset pricing, it is silent on the question of why are securities being priced they way they are. This is a critique that was espoused by Lawrence Summers, a macroeconomist who introduced the “Ketchup Economics” analogy. A no arbitrage framework merely states that 2 small bottles of ketchup must equal the price of one large bottle of ketchup. Yet the price of ketchup is based on demand and supply conditions like the yield of tomatoes, labour costs, packaging costs, consumer demand for ketchup and so on. While it is good to know that one is able to invest in a preferred security that is not mis-priced vis-a-vis a similar security, the no arbitrage framework still hasn’t told us the source of our investment compensation.
The discomfort from the no-arbitrage framework has thus encouraged the development of a first-principles based framework to think about asset pricing. Under this approach, microeconomic foundations are introduced to help price assets. Theorists then postulate a model where a utility-maximising agent with characteristic preferences, risk-aversions operate. Axioms (assumed to be true and not questioned) are introduced to provide the model with structure, and then the decision taken by this modeled agent is then evaluated to assets how assets are priced in the world described by the model.
The beauty of this approach is that it provides a demand and supply conditions narrative. It allows us to isolate fundamental risk-sources and tell a story of why certain stocks offer higher returns (it is technically invalid to use price levels, but higher discount rates mean that stocks are cheap, as prices and discount rates move in opposite directions). We will revisit this notion in greater detail when we present Modern Portfolio theory and its extensions, but for now, the key takeaway is that under this framework, averse risks are compensated with higher returns.
The attraction of this approach have given rise to the subfield of empirical asset pricing, where researchers attempt to find risk-sources that can help explain the return of assets. However, substantive criticisms remain. Some of the empirical asset pricing models are not purely derived from first-principles,rather, some researchers might have explored and constructed data series based on their intuition in order to extend the standard asset pricing models. However, as critics note, such an approach is essentially devoid of an economic interpretation. After all, a data-mining approach is vulnerable to breakdowns, since we have no understanding of the underlying process that generates the statistical relationship between the series that we are studying. Sophisticated econometrics models are useful in helping resolve disagreements, but are never a substitute to the role of theories in attempting to approximate truth. Behavioral finance concepts that built off psychology are realistic when presented in isolation, but proves to be a formidable task to incorporate into a standard asset-pricing model.
While these two frameworks in investment management have their own deficiencies, the fact is that investors planning their investment strategies for retirement could still make use of them rather than to grope for suitable investments in the dark. An awareness of the merits and critical weakness aids in asking the right questions and getting the right answers, and being able to critically discuss options with an investment adviser is key in making sure that investors are well-equipped to avoid assets that are ill-suited for them.