Risk Asset

Risk Asset Definition

Before we dive into risk asset definition, let's consider what an asset is.

This is an example of an explicit payment as you receive monthly monetary flow from renting your real estate property.

There is also the implicit form through which you receive monetary value from your asset.

That is, the monetary benefits of owning such an asset are realized once the asset is sold.

An asset could be subject to either capital gains or losses, which gives rise to risky assets.

While owning assets could be very beneficial and enable you to get generational wealth, it could also be risky, leading to capital losses.

In addition to risky assets, there are also risk free assets.

However, you should be aware that risk free assets provide way lower returns than risky assets.

Risk Asset Formula

The risk asset formula is the fraction of money invested in risky assets multiplied by the standard deviation of the asset.

To reduce risks, an investor decides to invest their money between a risky asset and a non-risky asset.

Let's consider an investor who invests in Treasury bills and in the stock market.

The expected return on the investor's portfolio will be as follows:

\( R_p = bR_s+(1-b)R_t \)

Where \(b\) is the portion of the money invested in stocks and \((1-b)\) is the portion of the money invested in T-bills.

\(R_t\) is the expected return on T-bills, and \(R_s \) is the expected return on stocks.

The return on the investor's portfolio is 7%. What about the risk the investor faces?

The way to measure the risk the investor faces is by using the standard deviation.

Think of it as the deviation from the asset's usual (standard) return. If the asset has a high standard deviation, it's riskier.

We will denote the standard deviation of an asset by sigma.

The risk that the investor faces in his portfolio is:

\( \sigma_p = b\times\sigma_s \)

Where \( \sigma_p\) is the standard deviation of a portfolio and \(b\) is the portion of the money invested in stocks. Since the risk free asset has zero standard deviation, the only one that matters for the investor now is the standard deviation of the stock market - \( \sigma_s\).

Let's reconsider the formula of the expected return on the investor's portfolio.

\( R_p = bR_s+(1-b)R_t \)

Using some basic math, we can rearrange the formula.

\( R_p = bR_s+(1-b)R_t = bR_s + R_t - bR_t = R_t + b(R_s-R_t)\)

From the formula of risk on the investors' portfolio, we know the following:

\( b=\frac{\sigma_p}{\sigma_s} \).

Therefore,

\( R_p=R_t + \frac{(R_s-R_t)\times\sigma_p}{\sigma_s} \)

This equation is a budget line. It's a function that describes what happens to the returns on a portfolio when there is a change in risk.

Fig. 1 - Budget line of an investor choosing between T-bills and stocks

Figure 1 shows the budget line of an investor who chooses to invest between T-bills and stocks. The budget line represents the investor's choices between risk and the expected return on a portfolio.

When risk increases, the expected return on his portfolio increases as well. But to have his expected returns increase, the investor faces much more risk. Hence, he is exposed to more significant losses. This is known as the price of risk.

If the investor were risk-verse, the investor would choose to invest all their money into T-bills and generate an expected return of \(R_t\), as \(b=0\).

If the investor wanted some risk, meaning they are risk-loving, they would invest all the money into stocks where \(b=1\). The expected return on this investor's portfolio would be \(R_s \).

Risk Asset Examples

There are many examples of risky assets. Usually, assets that are risky generate higher returns as well as higher losses. A famous saying among investors is that 'the higher the risk, the higher the return'.

Risk Asset Management

One of the main risk asset management strategies involves having the money invested in different asset classes to mitigate the risk an asset carries.

Fig. 2 - Managing risk

Figure 2 illustrates how an investor manages risk faced in their portfolio by choosing between different levels of risk and different levels of expected return. The portfolio of this investor consists of stocks and T-bills.

• If the investor wanted to go full-on risk and maximize their return, they would choose to invest all their money in stocks and get a return of \(R_s\).
• If they didn't want to take risks and get a guaranteed return, the investor chose to invest all of their money in T-bills at \(R_t\).

However, the investor manages the risk by investing parts of their money in T-bills and the other part in the stock market.

There are three indifference curves in the diagram above, and each curve details different combinations of risk and return that result in the same level of utility for the investor.

As risk is undesirable for the investors, the indifference curves slope upward. Therefore, a higher level of risk is associated with a higher expected return level to leave the investor with the same level of utility.

Amongst the three curves, indifference curve I₃ provides the highest degree of satisfaction, whereas indifference curve I₁ provides the least amount of satisfaction. In other words, the investor would rather be on indifference curve I₃ than any of the other three indifference curves.

However, as I₃ does not intersect with the budget line, the investor cannot choose indifference curve I₃. The investor can choose I₁, but I₂ gives the investor a higher level of utility, and therefore the investor decides to choose I₂.

The point where the I₂ intersects the budget line is the point that reveals the expected returns on the investor's portfolio and the standard deviation of his portfolio, in such a case, \(R_e\) and \(\sigma_e\).

Types of Asset Risk

There are three main types of asset risk: lower risk, moderate risk, and higher risk.

Lower risk are the type of assets that are associated with lower risk and lower return as well.

Moderate-risk assets are assets that are associated with moderate risk and moderate return.

Higher risks are assets that have higher returns but, at the same time, are riskier than other assets.

Figure 3 illustrates some types of assets and their degree of risk accordingly.