For one last time, I want to come back to the problem of whether you get a loan for your project under the assumption that the risk inherent in your project is stochastically independent of other investment risks. So this was our problem (see also here and here):
where is the repayment amount that you pay back to the investor in case of the project being successful. We argued (in a previous post) that the range of feasible interest rates is 12,5% to 200%. Anything outside that will certainly not be accepted by either the investor or by you.
Suppose that you and the investor are close to agreeing to an interest rate of just over 12,5%. Put yourself in the shoes of the investor for a moment. What might worry you in this case?
We can use the previous posts (one, two, three) on how financial markets deal with risk also to talk about insurance. In fact let us talk about a particular insurance problem. Suppose you live and own a house in Graz, or any other town with a river going through it. I believe Graz has not seen major flooding in a very long time, but with climate change all this could change. Also not having seen flooding in a long time does not mean there is no chance of it happening. And of course many towns in the world have fairly frequent and serious flooding events.
Suppose then that you live in one of these cities and are considering buying insurance against flooding. When I say “against flooding” I, of course, mean that the insurance will pay out some money in the event of a flood and that this amount is so that it covers the costs of all repairs that become necessary because of the damage caused by the flood. Suppose furthermore that there is no other insurance already in place (such as the local or national government paying out some emergency funds in such cases). In this post I want to address the following question: Will you have to pay a large risk-premium on your flood-insurance?
Recall the problem we had in the previous two posts (here and here). You are considering undertaking a worthwhile but risky project and need some startup money in order to do it. Investors give your project an 80% chance of succeeding and a 20% chance of failing. The problem can be summarized in the following table, where is the repayment amount that you pay back to the investor in case of the project being successful. If it is unsuccessful you pay nothing, because you have nothing. You “default” on your loan in that case. This is the risk the investor takes on when she or he gives you this loan.
In the previous post we considered the case that this risk inherent in your project is stochastically independent of the risks in other potential investment opportunities. In this case we figured out that the interest rate you might get for your project might be as low as 12.5% (but certainly not below that). This is so low that, due to the risk in the investment, investors expect actually a zero return on their investment. The actual interest rate would then probably be a bit higher, determined by supply and demand.
All this depends, however, on the fact the risk is stochastically independent of other risks. Expressed differently, one could say that the financial market generates no risk premium on any stochastically independent risk in an investment opportunity. This is because investors can hedge independent risks away by diversifying their investment portfolio. They can invest small amounts in many such independent risks and then, by force of the law of large numbers, actually have no risk in their diversified portfolio.
In this post, which I am now finally getting to, I want to consider how this analysis changes when the risk inherent in this investment opportunity is not stochastically independent of other risks, but is correlated with them.
In the previous post we had the following problem. We were wondering about which interest rate we could expect to see for a loan for a particular risky project. You would like to get a loan, and an investor might like to give it to you. The question was, under what conditions you would get this loan, if you get it at all. Recall, that your project can turn out to be good or bad and that investors generally agree about the chances and consequences of either outcome. The problem can be summarized by the following table, where is the repayment amount that you pay back to the investor in case of the project being successful. If it is unsuccessful you pay nothing, because you have nothing. You “default” on your loan in that case. This is the risk the investor takes on when she or he gives you this loan.
We figured out that you will not accept the loan if the repayment amount is more than € 200.000 (that would be an interest rate of 200%). Because then you have nothing to gain from this project. In reality, you might not even accept anything close to 200%, but we will come back to this problem later.
We also figured out that the investor will (almost) certainly not accept an interest rate below 12.5%, as otherwise the investor expects a negative return on their investment and would then be better off just putting her or his money under a mattress or, I guess, in a safe or vault. By the way, for a very long time the Catholic Church (and other religions) considered positive interest rates morally wrong. In such a world, you probably wouldn’t get a loan for your great project, unless you find a way around this problem. And that would probably be a shame (see previous post).
In this post I want to think about whether an investor will really accept an interest of 12.5% (or slightly above) given that the investor now takes all the risk and at an interest rate of 12.5% only expects a zero return. The answer to this question, it turns out, all depends on whether the risk in this project is essentially stochastically independent of all other risks inherent in all other projects or not.
So far we talked a bit abstractly about markets. Yes, we used some specific products for examples, such as white wine, rental apartments, and perhaps airline pricing, but we have not yet developed a particular market model specifically for a particular product. In this post, I want to do this for a particularly important market: the market for money. This post gives a first account of the basic insights and ingredients that underlie our understanding of credit markets and financial markets. You will see, I hope, that what we have learned so far, especially about supply and demand, while not enough to understand these markets fully, was also not in vain. It will come in handy.
You may recall that the value of anything is really a subjective thing, something may be valuable to someone, but at the same time may be not valuable to someone else. In this post I want to investigate in what way, if any, in what way the gross domestic product (GDP) measures total “market” value.
Consider JK Rowling’s first Harry Potter book. I want to understand in this post how the production of this product enters the national “gross domestic product” calculation.