# Risk Aversion in Corporate Finance

There are certain risks that no amount of diversification can eliminate. *Specific risk* is any risk associated with an individual investment and holds the possibility of being eliminated or greatly minimized through diversification. Default risk on a bond, liquidity risk on the corporation underlying a stock, and the risk of a building losing value in the real estate market are all specific risks.

You can minimize specific risks through diversification. This strategy can’t stop the entire economy as a whole from going down the toilet, though. Sometimes, no matter how perfect an individual asset is or how well a portfolio is diversified, a nation’s economy goes down the crapper and everything loses value. The risk of that happening is called *systematic risk.*

To minimize systematic risk, you can either diversify internationally (national economies tend to change at different rates just like individual investments), become very good in economics (many people tried to warn everyone about the coming 2007 financial collapse), or just hope to get very lucky.

You may ask, though, “Didn’t you say something about risk-free investments in the chapter on bonds?” Why, yes. Short-term, fixed-rate, highly liquid assets issued by organizations with great credit scores are considered to be risk-free.

Basically that boils down to T-bills, which mature in as little as a few weeks but no more than one year, are issued by the government (which has a very high credit score), have a fixed return, and can be easily sold. The amount of risk associated with T-bills is so small that they’re considered risk-free.

The problem is that they also offer very, very low returns, on par with CDs or some savings accounts at credit unions. Still, you do get a financial return on these without incurring any risk, and risk-free assets are the assets against which all other investments, considered risky assets, are compared.

The risk-free rate is the annual return on a risk-free asset, so any investment that has more risk than the risk-free asset must also offer at least proportionally as much return. Otherwise, it’s in the best interest of the investor to buy only risk-free investments.

How much risk a corporation takes depends on how risk averse the investing manager of that corporation is. Many people are willing to take on far more additional risk just for the chance of generating a little bit of extra return.

Some crazy people take on extra risk when they could generate just as much financial yield from a lower-risk investment. Some onlookers think that those individuals are addicted to the risk, kind of like compulsive gamblers.

Often the amount of risk aversion that a corporation has depends on its timeline. Portfolios with short-term goals are usually more risk averse because they have less time to make up for any losses. Long-term portfolios can ride out any losses from systematic risk by waiting for the economy to regain strength.

Exactly how do you measure an investor’s risk aversion? Well, simply asking investors wouldn’t work. Saying “very averse” is a bit subjective, so it doesn’t help us mathematically.

There are a number of ways to measure how risk averse a particular corporation or investor is. Insurance agents like to measure risk aversion in terms of how much insurance a person needs, often measured as the total potential loss should the insured asset/person experience a worst-case scenario. Many financial advisors measure risk aversion in terms that don’t actually utilize a risk function, instead opting to utilize only their time horizon.

They choose the lowest-risk investments available that are likely to generate the necessary returns within the time horizon. Those who simply seek to maximize returns for their client often take the average cyclical duration of investments into consideration; in order to avoid nearing the end of the portfolio time horizon during a recession, they gradually shift the focus of the portfolio toward less risky investments as the end gets closer.

Modern portfolio theory utilizes something called an aversion function. An *aversion function* is measured by determining how much additional return a corporation must think is possible to be willing to take on just one additional unit of risk. Risk is measured, in this exercise, as the probability of loss (*p*), while (1 – *p*) is the probability that no loss will be experienced.

This is true because 1 = 100%, and *p* is any number between 0 and 1. So, if *p* is 0.4, there’s a 40 percent chance of loss and a 60 percent chance (1 – 0.4) that no loss will be experienced. This strategy is completely hypothetical, however, as a method of measuring risk aversion.

In the extreme, a corporation that’s completely neutral to risk — in other words, willing to take on any amount of risk for additional gain — has a risk aversion of 0. This is often true for extremely low-risk assets, such as the difference between a Treasury bill and a Treasury note. A risk aversion of less than 0 means taking on additional risk without the expectation of additional gain, which is insane.

So, as a simple matter, the aversion function is a curved line that measures how much additional return must be generated for a single unit of additional risk. The function changes depending on how much risk has already been incurred by the corporation, but is measured by dividing the percentage change in expected returns required by the corporation to take on a percentage change in risk.

Another way to measure risk aversion is in terms of the risk premium demanded by an investor. Mathematically, it looks like this:

A= [E(r_{m}) –r_{f}] / σ_{m}_{}

where

A= Risk aversion

E(r_{m}) = Expected returns on risky assets required to attract the investor

r_{f}= Rate of return on risk-free assets

σ= The amount of risk in risky assets_{m}

This method provides more of a spot ratio of risk aversion rather than the dynamic one provided in the previous method. Folks who are mathematically inclined combine the best of both methods. The goal is simply to help you understand the role of risk aversion; that is, that investors who are more risk averse require higher returns to invest in riskier assets than investors with low risk aversion.