I’m gonna talk about the risk and return of single asset.
When we invest, our target is to make good return.
Return Defined
Return represents the total gain or loss on an investment.
The most basic way to calculate return is by using the following formula.
cash flow received plus current value minus previous value, over previous value.
Current value is the sale price, while previous value is the purchase price. The difference between purchase and sale prices is called capital gain. So, this formula can also be expressed as
return equals current income plus capital gain over purchase price.
Let’s take an example.
Johnny wishes to determine the returns on two of the company’s projects, Project X and Project Y.
Project X was purchased 1 year ago for $20,000 and currently has a market value of $21,500. During the year, it generated $800 worth of after-tax receipts. Project Y was purchased 4 years ago; its value in the year just completed declined
from $12,000 to $11,800. During the year, it generated $1,700 of after-tax receipts.
For Project X, $800 is the current income, $21,500 minus $20,000, you will get the capital gain,
and $20,000 is the purchase price. By applying the formula, you will get the return, 11.5%.
Similarly, for Project Y, you will get the return, 12.5%. So, based on the answers, we may conclude that, Project Y has a higher return than Project X.
There are in fact two types of return.
First is expected return. This is the return that an investor expects to earn on an asset,
given its price, growth potential, etc.
Second is Required Return.
This is the return that an investor requires on an asset, given its risk and market interest rates. Return of a single asset: Expected return
The expected value of a return, r-bar, is the most likely return of an asset.
It can be calculated based on this formula, in which we take summation
of all return of the outcome times the probability of occurrence of the outcome.
Let’s apply this formula. Under possible outcomes, pessimistic means the estimated lowest return, most likely
means the mostly attainable return, while optimistic means the estimated highest return.
The probability for pessimistic is 0.25, most likely is 0.5, while optimistic is 0.25.
For Asset A, the lowest return is 13%, most likely return 15%, optimistic return 17%.
By taking probability times returns of each possible outcome, you will get the
weighted values for each possible outcome. Sum up these, you will get the expected return, 15%.
Do the same for Asset B, in which its lowest is 7%, highest is 23%,
you will get the expected return also 15%.
Historical Returns for Selected Security Investments (1926-2003)
Based on past studies, historical returns for selected security
investments between 1972 and 2020 are as follow.
Small-cap stocks have the highest average annual return, 12.7%.
Followed by large-cap stocks, with 10.8%.
Long-term corporate bonds (and government bonds) have lower risks,
that’s why the returns are also lower.
Treasury bills have a return which is similar to bank fixed-deposit interest rate.
Risk Defined
After talking about return, now let’s talk about risk.
In the context of business and finance, risk is defined as the chance of suffering a financial loss. Risk is not a loss, risk is only the chance of suffering a loss.
Assets, no matter they are real assets or financial assets, which have a greater
chance of loss are considered more risky than those with a lower chance of loss.
Risk may be used interchangeably with the term uncertainty to refer to the variability
of returns associated with a given asset. Take note here, the risk is the uncertainty.
Risk Preferences
Risk preference is how people feel about taking risks. There are three types of risk preferences.
Risk-averse investors refer to those conservative investors, who prefer the preservation of capital
over the capital gain. They are unwilling to accept risk in their investment. Usually, they only accept low-risk investments with low returns. Risk-indifferent investors are also called risk-neutral investors. They evaluate investment alternatives by focusing solely on potential gains, regardless of the risk. Simply speaking, as long as the investments can provide the returns
they want, they will invest, no matter the risk is high or low. We may say, risk-indifferent investors don’t care about risk, they only care about return.
Risk-seeking investors refer to those aggressive investors,
who prefer the capital gain over the preservation of capital. They are willing
to accept high risk in their investments, as they only aim for high-return investments.
Risk of a Single Asset
How do we compare the risk of a single asset?
For example, Peter wants to choose the better of two investments, Asset A and Asset B. Each
requires an initial outlay of $10,000, and each
