Rate of Return
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What is Rate of Return?
The rate of return is a measure that quantifies the net gain or loss of an investment over a defined timeframe. The Rate of Return is presented as a percentage of the initial investment amount. It is determined by calculating the percentage difference between the investment's value at the beginning of the period and its value at the end of the period.
The rate of return concept can be extended to diverse investment vehicles such as real estate, bonds, stocks, and even unconventional assets like LEGO sets. It is applicable to any asset that is acquired at a specific time and yields a cash flow in the future. Assessing investments often involves comparing their historical rates of return with similar investments to identify the most attractive opportunities.
Rate of Return Formula
The formula for calculating the rate of return is as follows:
This basic return is sometimes referred to as the growth rate or alternatively as the Return on Investment (ROI). If you also take into account the impact of the time value of money and inflation, the real return can be defined as the net amount of discounted cash flows (DCF) received from an investment, adjusted for inflation.
Simple Example of a Rate of Return Calculation
The return can be calculated for any investment involving any type of asset. Let's consider the example of purchasing a house to understand how to calculate the return. Suppose you buy a house for CHF 1,000,000.
After ten years, you decide to sell the house and manage to sell it for CHF 1,250,000 after deducting all fees and taxes. The simple return on the purchase and sale of the house is then calculated as follows:
What if instead you sold the house for less than what you paid for it, let's say for CHF 750,000? In this case, you can still use the same formula to calculate your loss or negative rate of return:
The Rate of Return for Stocks and Bonds
The calculation of the rate of return for stocks and bonds differs slightly. Let's assume an investor purchases a stock for CHF 100 per share, holds the stock for five years, and receives a total of CHF 5 in dividends. If the investor sells the stock for CHF 120, the profit per share is CHF 20 (CHF 120 - CHF 100). Additionally, the investor has earned CHF 5 in dividend income, resulting in a total profit of CHF 25 (CHF 20 + CHF 5). Therefore, the rate of return for the stock is a profit of CHF 25 per share divided by the cost of CHF 100 per share, which equals 25%.
On the other hand, consider an investor who pays CHF 100 for a bond with a 5% coupon and a face value of CHF 100. The investment generates CHF 5 in interest income per year. If the investor sells the bond prematurely after two years for CHF 110, having earned a total of CHF 10 in interest, the investor's yield is the profit of CHF 10 from the sale plus CHF 10 in interest income (2 x CHF 5) divided by the initial investment cost of CHF 100, resulting in a yield of 20%.
How to Calculate the Rate of Return in Asset Management
When calculating the rate of return for a securities portfolio, two commonly used metrics come into play. One of them is the time-weighted rate of return (TWR). The TWR is particularly useful for comparing asset managers, as it measures the performance of the portfolio relative to other asset managers. It does so by excluding or disregarding the impact of cash flows, such as deposits and withdrawals, over which the asset manager typically has no control. However, it's worth noting that the TWR can sometimes be misleading, as it may show a positive rate of return even if the portfolio is in a loss, or vice versa. Therefore, its primary purpose is to facilitate comparisons between asset managers rather than serving as an accurate measure of the portfolio's rate of return.
For an accurate calculation of the actual average rate of return of a securities portfolio, the money-weighted rate of return (MWR), is more suitable. Unlike the TWR, the MWR takes into consideration the impact of cash flows. A comprehensive assessment of a portfolio's performance includes both the time-weighted rate of return to evaluate the asset manager's performance and the money-weighted rate of return to gauge the effective average rate of return of the securities portfolio.
Real Return vs. Nominal Return
The simple rate of return is also referred to as the nominal return because it does not account for the effect of inflation over time. Inflation reduces the purchasing power of money, meaning that, for example, one Swiss Franc in ten years will not have the same value as one Swiss Franc today.
Discounting is a way to account for the time value of money. Once the effect of inflation is considered, we refer to it as the real return (or inflation-adjusted return).
Real Return vs. Compound Annual Growth Rate (CAGR)
A concept closely related to the simple rate of return is the compound annual growth rate (CAGR). The CAGR represents the average annual return of an investment over a specific period that extends beyond one year, which means that when calculating it, the growth over multiple periods needs to be taken into account.
To calculate the average annual growth rate, we divide the value of an investment at the end of the relevant period by the value at the beginning of that period, raise the result to the power of one divided by the number of holding periods (e.g., years), and subtract one from the subsequent result.
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