Back of the Envelope

Observations on the Theory and Empirics of Mathematical Finance

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While most of you seemed rather groggy today (unsurprisingly, more so in ‘C’ than in ‘A’ ), but whether or not you plugged in to what was going on, it should be obvious to you all that finance should matter to you.

Most of you are here with a goal to make good money; you spend money, and also know a thing or two about investing in the future. The fact that you are here at WIMWI is a testimony to that. It also shows that you understand the risks implicit in one’s choices. How is that? By choosing to come here you are sacrificing not only two years of your earnings (your opportunity cost), but you are also taking a ‘risk’ in ending up with a future that maybe sub-optimal in an economic sense.

At the same time, given the ‘signal’ that the ‘brand name’ of WIMWI provides,  I am sure that is the least of your worries. If anything, the fact that you choose to come here is an indication that you value a future that is less risky. Getting education in a place like WIMWI pretty much ensures that you’ll belong to the upper half of the tail of the income distribution whichever field you choose to work in. That is, you have chosen an alternative in life that potentially reduces your sensitivity to future risks. This is not to judge your choice, but to make you aware that you all ‘practice’ finance as you live your life even now. What we’ll do in this course would be to provide a context to your individual (economic) stories; provide you a ‘way’ to systematically and constructively think about making financial decisions.

Finance is a way of doing things. It is a technology. We are all familiar with the technology of calculus. We don’t think twice about taking derivatives – even though at a fundamental level it is actually a limit. So, just like knowing the language/tools of calculus allows us to find slopes of functions, velocity of an object and what-not, in this course we’ll build the language/tool-kit of finance.

Let’s recap the some of the examples/teasers that we posed today, and then some:

  1. Lottery: Say, you are lucky to end up with an unexpected windfall of money from a lottery or an endowment from your friends/family. And, say, you are given two options (that’s typically how lotteries get paid off) – get Rs. 20 lacs now or get it in 20 instalments of Rs. 1.5 lac each every year for the next 20 years. How do you answer this question? And more importantly, how do you think about answering such questions?
  2. Lottery and an investment opportunity: Say, you win the lottery but your reward is that you can either come to WIMWI for two years, or have your own start-up? What should you do? What’s the right answer? Again, finance not only tells you how to think about such questions using the language of finance, it also tells you that the answer to this question is same for everybody. Now, isn’t it amazing! It says whatever you preferences (read: utility curves) are – whatever they may be – the answer to this question is independent of that, and should be the same for everybody. We’ll see this result come out very soon.
  3. Retirement problem: Look forward and imagine you are 40, and by now a big-shot consultant with a 15 year’s experience behind you and earn as much a crore a year by then. You say you’ve had enough of slogging your back off and just want to retire by the time you are 50. How should you plan your retirement – that is, how much you should start saving/investing every year so that you have the same standard of living till the time you expect to live?
  4. Insurance: Why on earth does it make sense for insurance firms to pay your medicine and accident bills when clearly you don’t pay anything close to the insured amount as premium? Yes, it’s because of the  risk-pooling. The fact that risk can be spread across a bunch of people makes insurers willing to take on your individual risk. But think about the situations like the Japan’s nuclear reactor accident? And what about AIG who were insuring those contingencies with things like Credit Default Swaps?
  5. Valuing start-ups: Say, being a big shot MBA and all that, find that some of your scientist friends have come up with a cure for cancer. And your friends convince you that drug could really work on humans even though there is a probability attached to it. But you know that if the drug works then you are in for a lot of money – the market clearly is huge – and you value your firm close to that like a Dr. Reddy’s or a Ranbaxy. Does it make sense? Or should your start-up be worth less given the possibility of the drug failing? Could it be more? Should it?
  6. Betting Markets: Say, you are a bookie taking bets for the on-going India – West Indies test series. The experts believe that the odds for the series are stacked in India’s favour as 60:40 (and it shows by now doesn’t it). But some gullible fellow comes and offers you 300,00 INR, with the odds that he be given 200,000 if India draws the series. Clearly the odds are in your favor. But the thought of losing 200,000 makes you jittery. You also have some friends who are willing to bet on these odds but much smaller amounts. What should your strategy be? Should you take up that gullible fellow’s offer knowing very well you hate the idea of losing as big an amount as 200,000. Well, again, there is a unique answer to that question that finance provides. And you’d be surprised that the ‘right’ strategy makes sure you do not lose a single Rupee whoever wins.

There are just some examples of the problems that we can tackle using the technology of finance. But is there anything that is common to all these problems? Of course, the common element is finance itself, but that’s tautological. So what is it?

Well, other than the fact that all problems are about money obviously, all of them have two common elements: that of time and uncertainty. Yes, that’s what finance – well, the investment part of it in any case, helps us do. Whenever we are faced with a cash flow/monetary problem where there is both an element of time as well as that of uncertainty/risk, finance provides us with a kit to address these questions.

And, yes, this is relevant across management disciplines – for marketing (what product mix, how much to invest in advertising?) as well as for operations (how much inventory to hold?). Of course, the context decides the extent of the problem, but clearly the notion of time and uncertainty is implicit in all kinds of investments decisions across firms and across industries.

But isn’t that all of our examples posed above affect only a percent of our economy (in GDP terms)? For most of the population the only financial institution they are typically concerned with is their neighborhood bank. So what about consumption? Isn’t it true that at a very basic level all our decisions are about consumption? As we’ll see, the existence of financial markets allow not just firms but all consumers to be better off.

There is this beautiful Separation Theorem given by Irving Fisher that financial markets allow firm to separate their investment and financing decisions and consumers to separate their investment and consumption decisions. (This is one of the three separation theorems you’ll study in finance – the other two are the Mutual Fund Separation Theorem and Modigliani-Miller Capital Structure Irrelevance Theorem).

It is great because it allows firms to worry about investments on their merit without worrying about how the money is going to come from, and allow you to come to WIMWI (again, on its own merit) without worrying about where the money for that is going to come from. We’ll ‘prove’ that later (well, not really prove prove, but kinda show that it holds). Just remember to revisit your MRSs and MRTs.

Some other things we talked about today:

Principal-Agent Problem in Finance

Shareholders (principal) own the firm, but managers (agent) run it. Their incentives, however, are not aligned, or needn’t be so. Shareholders want to maximize the value of their holdings (read: the stock price), but managers worry about their survival, their bonus/promotion, and short-term profits. This, however, may lead agents to select investment opportunities that may be beneficial to them in the short-run, but in the long-run may reduce shareholder value. This ‘moral hazard‘ is just one example of the principal-agent problem in corporate finance.

So, to make sure managers work in shareholders’ interests, the principals must monitor the agents. The resultant monitoring costs are called agency costs. Some of the way shareholders/markets have devised to reduce these costs is by taking measures like:

  • Choosing Board of Directors who select the top management and ensure that the goals of the guys they recruit (to run the firm) are aligned with those of the shareholders. The top management then selects the senior management and so on and so forth.
  • Linking a substantial portion of the senior/top management’s pay to the firm’s performance / share price.
  • Providing stock options which are directly linked to the firm’s value.

Also, competition in the job market ensures that managers work in the shareholders’ interests and thereby increase their ‘market value’ in the eyes of the other companies’ top management / Board of Directors. May be there is a lesson for each of you in this – in how you plan your career path. Whether to maximize short-term gain by changing jobs quickly, or work ‘for’ the firm you are working in so that you are considered a future CEO material.

The principal-agent problem is an example of the consequences of information asymmetry in economics. One of the other examples that I guess you would be studying in your microeconomics course is the agency problem, where, for example, the owner of a commodity has more information than the seller. So, the buyer believes that he/she is getting passed on an inferior product, and the seller wants to hide the deficiencies, so the market fails to clear. (The guy who first systematically tackled this problem, George Akerlof, won the Nobel Prize for his efforts). This problem (and his paper) also goes by the name of ‘Market for Lemons‘. (Old defective cars are also called lemons in the US.) The similar concerns of moral hazard apply when people buy medical insurance.

But what if you are in a non-finance Firm: Where do financial markets come in? Why should you worry?

At this point you may ask – all that separation theorem and the principal-agent problem and all that is ok, but why should financial markets matter to say, a marketing or an inventory manager in a non-financial firm?

Well, it should. In any firm, or industry you are employed in as a manager, you’ll be asked to make decisions where you’ll have to worry about what your competitors and suppliers are doing. You may hire a team of analysts in your department to that for you, but that would be highly inefficient. That’s not your ‘business’, right. These things are best left for specialized firms. And market price of securities of your competitors and suppliers contain that information (well, for the most part) – so for many a purposes how your competitor is doing could be told by just looking at their market performance.

A more direct example would be to consider, say, you are employed for a firm that serves its customers in global markets. In that case you have to worry about foreign exchange markets. And similarly if you work for an operations firm should (and do) worry about the happenings in the commodities markets. And there is the whole issue of hedging against the risk of things that you don’t want to worry about, or you are not an expert on. So for pure risk management purposes, even derivatives market should matter to you. As to how and why all this is true we’ll see in second half of the course.

Suggested Readings

  1. Models by Emanuel Derman
  2. My Life as a Quant by Emanuel Derman
  3. Capital Ideas by Peter Bernstein

PS: One of the other things we’ll impress upon throughout the course is the importance of simplicity of models (and it shows in the popularity of ideas which go as far back as to Irving FisherJohn Burr Williams and Harry Markovitz which are still in use today). As the boss says, ‘don’t try for a home-run when you can get the job done with a hit’.

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Written by Vineet

August 11, 2016 at 2:06 pm

Posted in Teaching: FM

Tagged with ,

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