Understanding Rates of Return

PDF Version

In the world of finance, "return" is the ultimate measure of success. It is the engine that drives wealth creation and the yardstick by which we evaluate our financial decisions. However, not all return metrics are created equal. A deep understanding of the nuances between different types of returns is fundamental for any serious investor looking to accurately assess performance and make informed choices.

The Foundation: What Is an Interest Rate?

At its core, an interest rate represents the price of time. The foundational concept of the time value of money tells us that a dollar today is worth more than a dollar in the future, simply because it can be invested to earn more money. An interest rate can be interpreted in several ways depending on the context. It can be seen as the minimum required rate of returnan investor demands to justify taking on the risk of an investment. It also functions as a discount rate, used to calculate the present value of future cash flows. Finally, it represents an opportunity cost—the return you forgo by choosing to spend or invest your money in one venture over another.

These rates are not arbitrary; they are meticulously constructed from several components that compensate investors for bearing distinct risks. The journey begins with the real risk-free rate, the theoretical return on a perfectly safe investment in a world with no inflation. From there, an inflation premium is added to protect the investor's purchasing power. Further layers are added to account for other dangers: a default risk premium compensates for the chance a borrower won't pay back their debt, a liquidity premium is demanded for assets that are difficult to sell quickly, and a maturity premium offsets the higher risk of long-term bonds, which are more sensitive to interest rate changes.

How to Measure Investment Returns

Once you've made an investment, the most basic way to measure its performance is the Holding Period Return (HPR). This calculation provides a total return, including both income and price appreciation, over the specific period the asset was held. While simple and useful for a single investment over a defined timeframe, its limitation is that it doesn't account for how long it took to earn that return, making direct comparisons between different investments challenging.

This leads to the crucial task of evaluating performance over multiple periods, where a simple average, known as the arithmetic mean, can be misleading. The arithmetic mean is best used for forecasting a single period's expected return, but it ignores the powerful effect of compounding and can be skewed by unusually high or low returns. In contrast, the geometric mean calculates the average compound growth rate per period. It is the superior method for measuring an investment's past performance because it provides a more accurate picture of the investor's actual experience. For example, an investment that gains 50% in year one and loses 50% in year two has an arithmetic mean of 0%, suggesting you broke even. However, the geometric mean reveals a loss, accurately reflecting that an initial $100 would have grown to $150 and then fallen to just $75. As a rule, the more volatile an investment's returns, the more the arithmetic mean will overstate the actual performance compared to the geometric mean.

A less common but still valuable metric is the harmonic mean. This specialized tool is most often used to find the average cost per share when an investor uses a dollar-cost averaging strategy, investing a fixed amount of money at regular intervals.

The Investor's Return vs. The Manager's Skill

A critical distinction in performance measurement arises when an investor adds or withdraws money from their portfolio. These cash flows can significantly distort return calculations, leading to the development of two different methods: the money-weighted and time-weighted rates of return.

The Money-Weighted Rate of Return (MWRR) is influenced by the timing and size of all cash flows, effectively calculating the portfolio's Internal Rate of Return (IRR). This metric measures the actual return earned by the investor, reflecting the combined result of the investment's performance and the investor's own decisions on when to add or remove funds.

In contrast, the Time-Weighted Rate of Return (TWRR) is designed to measure the compound growth rate of an investment while removing the distorting effects of cash flow timing. By breaking the evaluation period into sub-periods based on cash flow dates and linking the returns geometrically, the TWRR isolates the performance of the investment strategy itself. For this reason, it has become the industry standard for evaluating the skill of portfolio managers and making fair comparisons between them.

What Your Return Really Means

To truly grasp your investment results, it is essential to look beyond the headline number and ask what it represents. Always clarify if you are looking at a gross return or a net return. The gross return is the performance before any management fees or expenses are deducted, while the net return is the amount an investor actually keeps. Furthermore, returns are eroded by external forces. A pre-tax nominal return does not account for what you owe in taxes, whereas the after-tax return is what you are left with.

Perhaps most importantly, you must consider the impact of inflation. A nominal return may seem impressive, but the real return, which is the nominal return adjusted for inflation, tells you how much your purchasing power has actually increased. Finally, be aware of leveraged returns, which result from investing with borrowed money. While leverage can amplify gains, it equally magnifies losses, adding a significant layer of risk that must be managed with care.