Risk Shifting

That the amount of money and credit available are important determinants of asset prices.

Asset bubbles, or the inflation in the price of certain assets, are often started or catalyzed by an expansion of available credit. While later sections will go into more detail on asset bubbles, this section will present a concept called risk shifting which is another factor that can exacerbate asset bubbles. Risk shifting stems from the principal agent problem where the principal is unable to observe the actions of the agent, and is closely related to the moral hazard problem.¹¹ Risk shifting is common when the providers of investment funds are unable to observe the characteristics of investments made by a third party investor on the provider’s behalf.¹² Risk shifting can cause moral hazard which leads to the agent making overly risky investments. When this happens on a large scale it causes the prices of risky assets to be bid up

11 Allen and Gale, Understanding Financial Crises, 2007

12 Ibid

above their fundamental values.¹³ It follows that the amount of risk shifting, i.e. the amount of credit provided through third parties, is a major determinant of the severity of asset bubbles.

The following is an example of risk shifting provided by Allen and Gale (2007).¹⁴ It demonstrates how risky assets are bid up due to risk shifting by comparing a “fundamental”

case where investors invest on their own behalf, to an intermediated case where investors must invest through an unobservable third party. They consider it a “bubble” when the price of an asset rises above the price determined in the “fundamental” case.

In both cases there are two dates, t = 1,2. There are also two assets, a safe asset which is in variable supply, and a risky asset in fixed supply. For each 1 unit invested in the safe asset at date 1, the return is 1.5 at date 2. There is only 1 unit of the risky asset, and for this asset the return at date 2 is 6 with a 25% probability and 1 with a 75% probability. This leads to an expected payoff of 2.25 at date 2. Since there is a fixed supply on the risky asset, the price will be determined through bidding in the market. Let P represent the price of this risky asset.

In the fundamental case, each investor has 1 unit of wealth initially and invests her own wealth directly. Investors are risk neutral. The price of the risky asset can be determined by the following:

=

This shows that risk-neutral investors investing their own funds will only bid up the risky asset to the level where the expected rate of return is the same from each type of asset.

In the intermediated case, investors have no wealth of their own. They can borrow at a rate of 33.33%. The maximum amount that they can borrow is 1. If they borrow at t = 1, they pay back 1.33 at t = 2 if they are able to. If they are unable to pay back the full amount, they pay whatever they have. Because of this, borrowers are only interested in the upper part of the

13 Allen and Gale, Understanding Financial Crises, 2007

14 Ibid

distribution of returns on the risky asset. Lenders are unable to observe how the investors invest the money.

If an investor invests in the safe asset he will receive the following return after the loan is paid back:

1.5 – 1.33 = 0.17

If instead the investor was able to invest in the risky asset at the price determined in the fundamental case, he would be able to purchase 1/1.5 unit of the risky asset. In this case, the investor would have the following expected return:

.25((1/1.5 x 6) – 1.33) + .75(0) = 0.67

While the borrower would have the following expected return:

.25(1.33) + .75(1 x (1/1.5)) = .83

In this case there is only a 25% chance that the lender will get paid back in full. The interest rate that the lender charged is far too low to compensate for this amount of risk. In order to get the same 33% expected return, he would need to charge have a 232% interest rate as shown below:

.25(3.32) + .75(1 x (1/1.5)) = 1.33

For the borrower in this case, the risky asset with expected return 0.67 is preferred over the safe asset with a 0.5 larger payoff. For the lender, the expected return when the borrower invests in the risky asset is 0.5 less than when he invests in the safe asset. This 0.5 change in expected return is shifted from the lender to the borrower when the risk is shifted from the borrower to the lender. The lender cannot prevent this since the investment decisions of the borrower are unobservable.

In equilibrium with a variable amount of the safe asset and a fixed amount of the risky asset, the price of the risky asset will be bid up until the point where the expected return of borrowers is the same regardless of which asset they invest in. This is shown below:

.25((1/P) x 6 – 1.33) + .75 x 0 = .17 P = 3

In this case there is a bubble with the price of the risky asset being twice as high as it is in the fundamental case.

Another very relevant point brought up by Allen and Gale (2007) is that the amount of risk shifted depends on the how risky the asset is.¹⁵ This is often reflected in the price of the asset as the riskier the asset is the greater potential for shifted risk and thus the more the asset can be bid up before it returns the same as the safe asset. This is demonstrated in the extension of the previous example shown below.¹⁶

The situation is the same as in the previous example except that the return on the risky asset is 9 with a 25% probability and 0 with a 75% probability, reflecting additional risk. This yields the same expected return of 2.25 as in the earlier example. The price determination of the risky asset is:

.25(1/P x 9 – 1.33) + .75(0) = .17 P = 4.5

In this case, even more risk is shifted to lenders leading to an expected return for lenders of:

.25(1.33) + .75(0) = .33

In order for lenders to be properly compensated for this level of risk and still earn a .33 return, they would need to charge a 432% interest rate:

.25(5.32) + .75(0) = 1.33

Lenders will often proceed with lending despite this problem when there is a limited supply of the risky asset. This is because it will only be worth it for a relatively small proportion of borrowers to invest in the risky asset. The rest of the borrowers will invest in the safe asset and

15 Allen and Gale, Understanding Financial Crises, 2007

16 Ibid

be able to pay the lender back in full resulting in an expected return somewhere between the return where borrowers invest in the safe asset, and where they invest in the risky asset, depending on the supply of the risky asset.¹⁷

3. Overarching Issues related to Financial Crises