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.