Risk and Return in Financial Economics

Portfolio diversification can be defined as spreading investments across a range of alternative assets to reduce the overall risk of a given portfolio. This is achieved by selecting assets with varying degrees of correlation, as they are less likely to experience losses simultaneously.

Harry Markowitz is the founder of the modern portfolio theory.

Statistical measurement methods play a vital role in the practical application of modern portfolio theory. Some key measures include expected returns, variance, standard deviation, correlation, and covariance. These metrics provide valuable insights into individual assets’ performance and risk profiles and overall portfolio.

Financial return is the gain or loss generated by an investment over a specific period, expressed as a percentage of the initial investment amount. It represents the change in the value of an investment, which may result from capital appreciation, dividends, interest, or other income sources.

Financial return is the key metric investors use to evaluate the performance of investments and compare different investment options, as it provides a measure of rewards obtained from an investment relative to its initial cost.

In essence, a financial return quantifies the profitability of an investment and helps investors assess the effectiveness of their investment decisions. Simple percentage return calculation is straightforward. More importantly, we can present the main reasons why financial return calculation is critical.

First, investors use financial returns to evaluate the performance of different investment options, such as stocks, bonds, or real estate. By comparing returns, they can make informed decisions about where to allocate their resources to maximize their profits. As a second point, financial returns assist investors in understanding the level of risk associated with different investments. Higher returns often come with higher risks, so assessing the balance between risk and reward is crucial for successful investing. Finally, financial returns allow investors and managers to measure a portfolio’s performance or a specific investment over time. This can help them determine whether their investment strategies are effective or need adjustments.

Calculating the periodic return of a financial asset such as a stock, currency, or bond/bill is the most essential step in calculating the return of an asset.

Logarithmic return is a financial return measure used to determine the percentage change in an asset’s price over a specific period using logarithmic functions.

This type of calculation is preferred since it accounts for the compounding effect of investment returns.

The formula for one-period logarithmic return can be expressed as follows:

r(t) = ln[P(t)/P(t-1)]

Typically, when nominal asset values are small, linear and logarithmic returns tend to be similar. However, as the nominal asset values increase, these two measures start to diverge from each other.

One of the benefits of using logarithmic returns is their simplicity in the multi-period return formula.

In finance, short-term Treasury interest rates are considered risk-free or default-free because governments are assumed to be able to back their debts without defaulting. As a result, financial returns are often analyzed using this benchmark.

The difference between the returns on risky stocks and Treasury yields is the equity risk premium or excess return.

To calculate the excess return, one subtracts the risk-free rate (represented by the Treasury interest rate) at time t, denoted by r(F,t), from the stock’s return

The excess return, the difference between the risky and risk-free returns, is essential when evaluating investment performance.

Treasury yields typically represent the risk-free return and serve as an opportunity cost for holding a risky asset. When Treasury yields are high, most investors may be satisfied with these risk-free yields. Therefore, when treasury yields are high, demand for risky assets is lower. Stock market instruments are usually less prevalent in these periods. Since these yields are assumed to be risk-free, an investor looking for a better yield needs to take a higher risk. Consequently, stock markets and risky assets do not perform well during high interest rate periods. When treasury yields are low, the demand for risky assets such as stocks increases. It is generally hard to generalize, but a low-interest environment increases demand for stock markets.

Modern risk management heavily relies on financial return statistics. Investors can analyze the volatility of investments using these statistics and develop strategies to decrease risk.

Financial return statistics are critical from a financial application point of view for various reasons:

1. Return statistics are used to analyze and evaluate investment opportunities. These statistics help investors to compare different investment options, assess risk, and estimate potential returns.

2. Financial return statistics are used to monitor and manage investment portfolios. Investors can track the performance of their portfolios using these statistics and adjust to enhance their returns.

3. These statistics are used to measure the performance of investments and portfolios against benchmarks. By comparing the returns of investments and portfolios to benchmarks, investors can determine if they are achieving their investment goals.

4. Modern risk management heavily relies on financial return statistics. Investors can analyze the volatility of investments using these statistics and develop strategies to decrease risk.

5. Finally, these statistics are used for reporting purposes. They are used to report investment performance to financial regulatory bodies, stockholders, investors, etc.