There are a number of ways to calculate the investment return of an account. We discussed some of these (real return, total return and risk-adjusted return) in the Quantitative Methods section, and bond yields (yield-to-maturity, yield-to-call and the real interest rate) were discussed in the Fixed Income Secutities section. You will not be tested on the actual formulas, so we have not included them here (other than those provided for clarity). In this section we'll focus on return measures:

Return Measures

  • Return on investment (ROI) - this is the classic measure of performance, taking into account all cash flows (including dividends, interest, return of principal and capital gains). To calculate, simply divide the sum of all cash flows by the number of years the investment is held and then divide that amount by the original amount invested.

  • Risk premium - the risk premium is the higher return that is expected for taking on the greater risk associated with investing in a growth stock, versus a stock from a more established company.

  • Risk-free rate of return - the current rate for Treasury bills is typically used in calculations, such as risk-adjusted return and the Sharpe ratio.

  • Expected return - since the expected return is the average of the probability of possible rates of return, it is by no means a guaranteed rate of return. However, it can be used to forecast the future value of a portfolio and also provides a guide from which to measure actual returns.
    • It is an integral component of the Capital Asset Pricing Model, which calculates the expected return based on the premium of the market rate over the risk-free return, as well as the risk of the investment relative to the market as a whole (beta).

  • Benchmark portfolios - a common way to evaluate portfolio returns is to compare them to a benchmark, such as an index. These are the most common benchmarks:
  • Holding period return - this refers to the return for the period of time the investment was actually held. This can be more meaningful than an annualized rate of return, particularly for investments held short term. However, the standard deviation of returns depends on the holding period, since stock returns are more volatile over shorter periods of time. As a result:
    • the shorter the holding period, the greater the variability of the return

    • the longer the holding period, the smaller the variability of the return

  • Excess returns - this is the amount of return over and above what is expected based on the beta of the stock or portfolio.

  • Internal rate of return (IRR) - this is the interest rate that makes the net present value of a series of cash flows equal to zero. The internal rate of return can only be calculated by trial and error (or with a financial calculator) unless the investment has only a single cash flow, such as a zero-coupon bond. In that case the calculation is:

Internal rate of return = (Payoff/Investment) - 1

An example of this would be an investment of $1,000 that would return $1,100 in one year. The formula would produce (1100/1000) - 1, which equals 1.10 - 1, which equals 0.10 (10%).

Look Out!
The fact that internal rate of return presumes that the net present value of the inflows and outflows equals zero seems counterintuitive. It may be helpful to think of IRR as the discount rate at which the expected returns equal the initial investment. However, on the exam, the "net present value equals zero" will be the correct answer.

Exam Tips and Tricks
Consider these sample exam questions:

  1. An investor owns a small-cap stock with very low trading volume. The investor has a high level of:
    1. Business risk
    2. Market risk
    3. Liquidity risk
    4. Purchasing power risk

The correct answer is "c" - while there is also the potential of business risk, the best answer is liquidity risk because the question focuses on the low trading volume.

  1. Assuming that prices fluctuate throughout the investing period, the use of dollar-cost averaging results in a:
    1. Lower average cost per share
    2. Higher average cost per share
    3. Lower market price per share
    4. Higher market price per share

The correct answer is "a" - when prices are lower, more shares are bought, which results in a lower average cost per share.

  1. The Sharpe ratio measures:
    1. Risk-adjusted rate of return relative to portfolio volatility
    2. Level of portfolio volatility relative to a benchmark portfolio
    3. Level of investment return relative to the dollar amount invested
    4. Risk-adjusted rate of return relative to the risk-free rate of return

The correct answer is "a" - options "b" and "c" are clearly wrong. While "D" refers to the risk-free rate of return, which is a component of the Sharpe ratio, the definition is not correct.

  1. The method of evaluating investment returns that calculates the interest rate which discounts cash inflows and outflows to a present value of zero is called:
    1. Inflation-adjusted return
    2. Internal rate of return
    3. Total return
    4. Net present value

The correct answer is "b". Answer "d" is incorrect because the method referred to incorporates the concept of net present value, but it is not a definition of that term.


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