91Ó°ÊÓ

The concept of stock return calculation is fundamental to investing. In its basic form, the return on a stock is the amount of profit or loss generated by an investment in the stock over a certain period. It is typically expressed as a percentage of the investment's initial value. To calculate the simple return, you would subtract the initial value of the investment from its final value, divide by the initial value, and then multiply by 100 to convert to a percentage:

\textbf{Simple Return (%) =} \(\frac{Final\text{ }Value - Initial\text{ }Value}{Initial\text{ }Value} \times 100\).

In finance, we often extend this concept to account for various factors that might influence return, such as economic indicators like Gross National Product (GNP) growth and interest rates. For a more nuanced view, the factor model offers insights into how different economic factors influence the return on a stock. Through this model, we can dissect a stock's sensitivity to various economic variables using coefficients known as betas.

The beta coefficient, commonly referred to as 'beta', is a measure of how much a stock’s price tends to move with changes in the overall market or specific economic factors. A beta of 1 indicates that a stock's price tends to move with the market. A beta greater than 1 suggests that the stock is more volatile than the market - it moves more than the market. Conversely, a beta of less than 1 indicates that the stock is less volatile than the market. Moreover, a negative beta implies that the stock tends to move in the opposite direction to the market or factor in question. In relation to factor models, individual betas are assigned to multiple factors (such as GNP change and interest rate change in our exercise) to understand and predict a stock's sensitivity to those particular factors.

For example, a stock with a beta of 1.2 with respect to GNP changes will theoretically experience a 1.2% increase in its return for every 1% increase in GNP. Similarly, a beta of -0.8 for interest rates would mean the stock’s return decreases by 0.8% for each 1% increase in interest rates.

In factor models, economic indicators like the Gross National Product (GNP) and interest rates are thought to have a direct effect on stock returns. GNP measures the economic output of a country and is an indicator of economic health. Stocks tend to benefit from a higher GNP because it generally corresponds to increased business activities and potentially greater corporate profits. Therefore, a positive beta in relation to GNP suggests that a stock may see greater returns during times of economic growth.

The interest rate, on the other hand, affects a company's cost of borrowing and consumers' willingness to spend or save. A rise in interest rates often reduces profit margins for companies due to higher borrowing costs and can lead to decreased consumer spending. Stocks generally have a negative beta with respect to interest rates because as interest rates increase, stock returns tend to decrease, reflecting the higher cost of capital and reduced consumer spending.

The expected return is what investors anticipate they will earn from an investment, given the risks they have taken. This expectation is usually based on historical performance, the performance of similar investments, and underlying economic factors. Using factor models, the expected return can be projected by considering the sensitivity of a stock to various economic indicators and estimating their changes.

Actual return, however, refers to what is realized at the end of the investment period and can differ from the expected return due to unforeseen factors. Such deviations can result from a multitude of causes including but not limited to changes in GNP and interest rates that differ from expectations, as illustrated in our exercise. When actual economic conditions differ from the expected conditions, the actual return is recalculated using the same process as for expected returns but substituting actual changes in economic factors. This recalculated return provides investors with an updated projection of their investment performance based on real-world events.