Glossary: M01 — Rates and Returns

Module: M01 Formulas: Formula Sheet

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Interest Rate

The amount a lender charges for the use of assets, expressed as a percentage of the principal. Can be interpreted as a Discount Rate, Opportunity Cost, or Required Rate of Return.

LOS: 1.a | See: M01 — LOS 1.a

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Discount Rate

The rate at which investors discount future cash flows to arrive at their present value. A higher discount rate implies a lower present value.

LOS: 1.a | Related: Present Value

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Opportunity Cost

The value that investors forgo by choosing a particular course of action. If an investor can earn 8% on bonds, the opportunity cost of investing in stocks instead is 8%.

LOS: 1.a

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Required Rate of Return

The minimum rate of return an investor must receive to accept an investment. Composed of:

$r=r_f+\text{Default RP}+\text{Liquidity RP}+\text{Maturity RP}$

LOS: 1.a | See: Nominal Risk-Free Rate, Default Risk Premium, Liquidity Risk Premium, Maturity Risk Premium

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Nominal Risk-Free Rate

The rate of return on a risk-free asset (e.g., US Treasury bill). Composed of two components:

$r_f=\text{Real risk-free rate}+\text{Inflation premium}$

LOS: 1.a | Related: Real Risk-Free Rate, Inflation Premium

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Real Risk-Free Rate

The theoretical rate of return on an investment with zero risk and zero inflation. Reflects only the time preference for consumption — the compensation for deferring consumption.

LOS: 1.a | Note: Mainly theoretical; not directly observable in markets.

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Inflation Premium

The compensation investors require for the expected loss of purchasing power due to inflation over the investment horizon.

$\text{Nominal risk-free rate}=\text{Real risk-free rate}+\text{Inflation premium}$

LOS: 1.a | Example: If real rate = 2% and expected inflation = 3%, then nominal risk-free rate ≈ 5%.

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Default Risk Premium

The excess return that compensates investors for the risk that a borrower will not make promised payments in a timely manner.

LOS: 1.a | Example: Difference between corporate bond yield and Treasury yield of same maturity (the “credit spread”).

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Liquidity Risk Premium

The excess return that compensates investors for the risk of receiving less than fair value when an investment must be sold quickly.

LOS: 1.a | Example: Small corporate bonds trade infrequently → higher liquidity premium than US Treasuries.

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Maturity Risk Premium

The excess return that compensates investors for the increased sensitivity of the market value of debt to changes in interest rates as maturity is extended.

LOS: 1.a | Note: Longer maturity → greater interest rate risk → higher maturity premium.

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Holding Period Return (HPR)

The return earned from holding an asset for a single specified period (1 day, 1 week, 1 year, etc.).

$HPR=\frac{P_1-P_0+I_1}{P_0}=\frac{\text{Ending value}}{\text{Beginning value}}-1$

LOS: 1.b | See: Formula

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Arithmetic Mean Return

The simple average of a series of periodic returns. An unbiased estimator of the true mean return.

$\bar{R}=\frac{R_1+R_2+\cdots +R_n}{n}$

LOS: 1.b | Key: Always ≥ geometric mean (equality only when all returns are identical).

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Geometric Mean Return

The compound periodic rate of growth. Accounts for the compounding effect of returns over multiple periods.

${\bar{R}}_G=\sqrt[n]{(1+R_1)(1+R_2)\cdots (1+R_n)}-1$

LOS: 1.b | Key: Better measure of actual investment performance than arithmetic mean. Always ≤ arithmetic mean.

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Harmonic Mean

A measure of central tendency calculated as the reciprocal of the arithmetic mean of reciprocals. Best used when data consists of rates and ratios.

${\bar{X}}_H=\frac{n}{{\sum }_{i=1}^n\frac{1}{X_i}}$

LOS: 1.b | Key application: Dollar cost averaging, averaging P/E ratios. Always ≤ geometric mean.

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Money-Weighted Return (MWR)

The internal rate of return (IRR) of all cash flows in and out of a portfolio. Affected by the timing and size of cash flows.

LOS: 1.c | Use: Measures the investor’s actual experience. | See: Time-Weighted Return (TWR)

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Time-Weighted Return (TWR)

The compound rate of growth of $1 initially invested. Not affected by external cash flows.

$TWR=(1+HP{R}_1)(1+HP{R}_2)\cdots (1+HP{R}_n)-1$

LOS: 1.c | Use: Measures the portfolio manager’s skill (independent of client cash flow timing).

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Gross Return

The return earned by the investment manager before deduction of management and administrative fees. Trading expenses ARE included (deducted) in gross return.

LOS: 1.e | Key: Often used to evaluate manager skill because it excludes fees the manager doesn’t control.

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Net Return

The return after deducting management and administrative fees from the gross return.

$R_{\text{net}}=R_{\text{gross}}-\text{Management fees}$

LOS: 1.e

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Real Return

The return adjusted for inflation. Measures the increase in purchasing power.

$R_{\text{real}}=\frac{1+R_{\text{nominal}}}{1+\text{Inflation}}-1$

LOS: 1.e | Approximation: $R_{\text{real}}\approx R_{\text{nominal}}-\text{Inflation}$

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After-Tax Return

The return after accounting for taxes on investment income and gains.

$R_{\text{after-tax}}=R_{\text{pretax}}\times (1-\text{tax rate})$

LOS: 1.e

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Leveraged Return

The return on an investment that is partially financed with borrowed capital. Amplifies both gains and losses.

$R_L=R_p+\frac{V_B}{V_E}(R_p-r_D)$

where $V_B$ = borrowed capital, $V_E$ = equity capital, $r_D$ = borrowing cost

LOS: 1.e | Key: Leverage increases return only when $R_p>r_D$. It amplifies BOTH gains and losses.

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Continuously Compounded Return

The natural logarithm of the gross return. Used in lognormal asset pricing models.

$r_{cc}=\ln (1+HPR)=\ln \left(\frac{S_1}{S_0}\right)$

LOS: 1.d | Key: Always less than HPR for positive returns. Additive over time: $r_{0,T}=r_{0,1}+r_{1,2}+\cdots +r_{T-1,T}$

Related: Lognormal Distribution