Chapter VI: Measuring Investment Returns (Part 2)

Once you understand basic return calculations and compounding, you must learn how to measure returns over multiple periods, handle irregular cash flows, assess investment viability, and adjust for inflation, taxes, and risk.

1. Compounded Annual Growth Rate (CAGR)

In financial markets, the time value of money is always taken into account. If an investment provides a series of cash inflows, it is assumed that they can be reinvested to earn a positive return. Alternatively, if an investment does not have intermediate cash flows (such as a cumulative mutual fund or a zero-coupon bond), it is assumed to grow at an annual rate each year, compounded annually to reach its final value.

The Compounded Annual Growth Rate (CAGR) of an investment is the underlying compound interest rate that equates the end value of the investment with its beginning value over a specific time horizon.

• Formula: CAGR = ((FV / PV)^(1 / n)) - 1

  Where:

  • PV = Present Value (Beginning Value of investment)
  • FV = Future Value (End Value of investment)
  • n = Number of years (Holding period in years)

2. Extended Internal Rate of Return (XIRR)

The standard CAGR formula is highly effective when you are only dealing with a single beginning value and a single ending value over a fixed number of years. However, real-world portfolios usually experience multiple cash inflows and outflows (such as systematic investments, partial withdrawals, or lump-sum additions) at irregular intervals.

• Definition: The XIRR function is particularly useful when CAGR has to be computed for a series of multiple cash flows, rather than with just a beginning and ending value of the investment.
• Application: XIRR for a particular set of irregular cash flows can be calculated in Excel using the built-in XIRR formula.

3. Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is an alternative way to express the compounded return of an investment.

• The Scenario: Assume that an investment has a number of cash inflows (returns) occurring over a period of time against an initial cash outflow (investment) made at the very start.
• Definition 1: IRR is the inherent rate at which all the cash outflows compound to become equal to the cash inflows.
• Definition 2: IRR is the discount rate at which the present value of future cash inflows from an investment exactly equals the present value of the cash outflows.

4. Net Present Value (NPV)

Net Present Value (NPV) uses the core concept of the time value of money to evaluate the financial viability and profitability of an investment option.

NPV Mechanics

If an investment decision results in a cash outflow at the initial stage and a series of cash inflows over a period of time, the NPV is calculated as the difference between the present value of the cash outflows and the sum of the present values of the inflows that accrue over that period.

• The Discounting Rate: The discounting rate used in the calculation of the NPV is the required rate of return from the investment. This rate can be customized to reflect the specific risk level in the market.

NPV Decision Rules

An adviser can recommend an investment based on the resulting NPV:

• Positive NPV (NPV > 0): This implies that the investment is viable and worthwhile because it meets or exceeds the required rate of return.
• Negative NPV (NPV < 0): This indicates that the investment will fail to meet the required rate of return and should be avoided.

Constraints of Using NPV

1. Determining the Discount Rate: The primary constraint in using NPV is the difficulty of determining the appropriate required discounting rate.
2. Assumption of Constant Rates: NPV assumes that the discounting rate remains constant over the entire life period of the investment, which may not hold true in dynamic market conditions.

5. Holding Period Return (HPR)

The Holding Period Return (HPR) is the total return earned on an investment during the specific period over which it was purchased and held by the investor. Unlike annualised returns, HPR focuses purely on the actual duration of the holding period, utilizing the portfolio values at two chosen points in time.

• Formula: HPR = (Cash Inflows during the period + Capital gains) / Beginning Value of investment

  Where:

  • Cash Inflows = Intermediate income such as dividends or interest received.
  • Capital Gains = End Value of investment - Beginning Value of investment.

6. Nominal vs. Real Rates of Return

An investment's performance must always be evaluated in the context of purchasing power.

• Nominal Rate of Return: This is the return on an investment expressed as a standard percentage rate, without any adjustment for the effects of inflation.
• Real Rate of Return: When the nominal rate is adjusted to strip out the effects of inflation, it is known as the real rate of return. Inflation erodes the purchasing power of money over time; hence, the real rate of return represents the true growth of an investor's purchasing power.

7. Tax-Adjusted Return

Taxes are a critical friction point that reduces the actual wealth accumulated by an investor.

• Definition: Tax-adjusted return is the return earned on an investment after all applicable taxes have been paid by the investor.
• Significance: Since taxes actually reduce the net cash in the hands of the investor, it is absolutely necessary to calculate the tax-adjusted return to obtain a realistic view of the actual returns earned.

8. Risk-Adjusted Return

The relationship between risk and return is direct, meaning that investors who choose high-risk investments expect to be compensated with higher returns. Risk-adjusted return relates the absolute return generated by an investment to the specific amount of risk taken to generate it.

Advisers use two key risk-adjusted metrics to compare portfolios:

1. Sharpe Ratio

The Sharpe Ratio measures the excess return generated per unit of total risk.

• Formula: Sharpe Ratio = (Portfolio return - Risk free return) / Standard deviation of portfolio
• Risk Metric Used: It uses Standard Deviation (a statistical measure of total risk, representing the dispersion of observed returns around the average return over a time period).

2. Treynor Ratio

The Treynor Ratio measures the excess return generated per unit of systematic market risk.

• Formula: Treynor Ratio = (Portfolio return - Risk free return) / Beta of portfolio
• Risk Metric Used: It uses Beta (a measure of the volatility in the price of an investment relative to the overall market benchmark).

NISM Exam-Relevant Terms to Remember