READING 1 RATES AND RETURNS

Question 1

What do interest rates measure?

Answer 1

Interest rates measure the time value of money the compensation required for deferring consumption or accepting risk in financial securities.

Question 2

What determines equilibrium interest rates?

Answer 2

The intersection of supply (savers/lenders) and demand (borrowers) in financial markets. It’s the rate where the market clears (required return = market return).

Question 3

What is the real risk-free rate?

Answer 3

A theoretical rate with:

No inflation (purchasing power constant).
No default risk (guaranteed repayment).
Reflects pure time preference (reward for waiting).

*Used in models like CAPM

Question 4

What’s the difference between real and nominal rates?

Answer 4

Nominal Rate: Observed rate (includes inflation premium).
Real Rate: Nominal rate adjusted for inflation (true purchasing power).

(1+Nominal) ≈ (1+Real) × (1+Inflation)

T-bills are nominal risk-free (include inflation).

Question 5

What risks increase the required rate of return?

Answer 5

Default Risk: Borrower fails to pay.
Liquidity Risk: Can’t sell quickly at fair value.
Maturity Risk: Longer-term bonds have more price volatility.

Required Return ≈ Nominal Risk-Free Rate + Risk Premiums

Question 6

Are T-bill rates real or nominal risk-free rates?

Answer 6

Nominal risk-free they include an inflation premium but no default risk.

Why Not Real? Expected inflation is embedded in T-bill yields.

Question 7

Why do longer-term bonds have higher yields?

Answer 7

Maturity risk premium compensates for:

Greater price sensitivity to interest rate changes.
Uncertainty over future inflation/default risk.

Question 8

What are the components of a security’s required interest rate?

Answer 8

Real Risk-Free Rate (RRFR)
+Inflation Premium

+Default Risk Premium
+Liquidity Premium
+Maturity Risk Premium

Nominal Rate ≈ RRFR + Inflation + Risk Premiums

Question 9

Why does the real risk-free rate reflect “time preference”?

Answer 9

It quantifies how much society prefers current consumption over future consumption.

High RRFR = Impatient population (demands high reward to save).
Low RRFR = Patient population (willing to defer consumption).

Question 10

How does liquidity risk affect corporate bonds vs. T-bills?

Answer 10

T-bills: Near-zero liquidity risk (deep market).
Corporate bonds: Higher liquidity risk → higher yield demanded.

Question 11

Why are long-term bonds more sensitive to rate changes?

Answer 11

Duration risk, longer maturities have more cash flows exposed to discount rate changes.

Question 12

How is the inflation premium determined?

Answer 12

By expected future inflation (not past inflation).

Question 13

What’s the simplified formula for the real rate?

Answer 13

Real Rate ≈ Nominal Rate − Inflation

Question 14

Rank asset classes by risk premiums (low to high):

Answer 14

1. T-bills (nominal risk-free)
2. T-bonds (+ maturity risk)
3. Investment-grade bonds (+ default risk)
4. High-yield bonds (+ higher default risk)
5. Equities (+ liquidity, business risk)

Question 15

What is the arithmetic mean return?

a) A weighted average of periodic returns
b) The simple average of periodic returns
c) A return adjusted for outliers

Answer 15

b) The simple average of periodic returns

The arithmetic mean is the sum of periodic returns divided by the number of periods. It’s an unbiased estimator of the true mean return.

Question 16

When is the geometric mean equal to the arithmetic mean?

a) When returns are volatile
b) When all periodic returns are identical
c) When outliers are removed

Answer 16

b) When all periodic returns are identical

The geometric mean equals the arithmetic mean only if there’s no variability in returns (all observations are equal).

Question 17

How does the geometric mean compare to the arithmetic mean for volatile returns?

a) Geometric mean > Arithmetic mean
b) Geometric mean = Arithmetic mean
c) Geometric mean < Arithmetic mean

Answer 17

c) Geometric mean < Arithmetic mean

The geometric mean accounts for compounding and is always ≤ arithmetic mean, with the gap widening as volatility increases.

Question 18

Q: What is the harmonic mean used for?

a) Calculating average portfolio returns
b) Average cost of shares purchased over time
c) Adjusting for inflation in returns

Answer 18

b) Average cost of shares purchased over time

The harmonic mean is used for dollar-cost averaging (e.g., fixed monthly mutual fund purchases).

Question 19

For non-identical values, how do the means rank?

a) Harmonic < Geometric < Arithmetic
b) Geometric < Harmonic < Arithmetic
c) Arithmetic < Geometric < Harmonic

Answer 19

a) Harmonic < Geometric < Arithmetic

Harmonic < Geometric < Arithmetic is a mathematical property (e.g., for returns: 2%, 5%, 8%).

Question 20

Why is the harmonic mean relevant to dollar-cost averaging?

a) It ignores volatility
b) It lowers the average share cost
c) It compounds returns

Answer 20

b) It lowers the average share cost

Buying fixed dollar amounts over time reduces average cost per share, which the harmonic mean captures.

Question 21

Which measure is most affected by outliers?

a) Geometric mean
b) Arithmetic mean
c) Harmonic mean

Answer 21

b) Arithmetic mean

The arithmetic mean includes all values, making it sensitive to outliers.

Question 22

What does a trimmed mean do?

a) Removes a percentage of extreme values
b) Compounds periodic returns
c) Adjusts for inflation

Answer 22

a) Removes a percentage of extreme values

A trimmed mean excludes a set percentage of the highest/lowest values to reduce outlier impact.

Question 23

How does a winsorized mean handle outliers?

a) Replaces them with the nearest non-outlier
b) Excludes them entirely
c) Doubles their weight

Answer 23

a) Replaces them with the nearest non-outlier

Winsorizing caps outliers at a certain percentile (e.g., 95th percentile).

Question 24

When should you use the arithmetic mean?

a) To measure compounded growth
b) To include all data points
c) To calculate average share cost

Answer 24

b) To include all data points

se the arithmetic mean when all values (including outliers) are relevant.

Question 25

When is the geometric mean preferred? a) For single period returns b) For multi-period compounded returns c) For risk-adjusted returns

Answer 25

b) For multi-period compounded returns The geometric mean reflects compounding over time (e.g., annualized returns).

Question 26

Why does volatility reduce the geometric mean? a) Compounding magnifies losses b) Arithmetic mean overestimates growth c) Both A and B

Answer 26

c) Both A and B Volatility drag (compounding asymmetric returns) lowers the geometric mean below the arithmetic mean.

Question 27

For returns of 10%, 20%, and -5%, which mean is largest? a) Arithmetic b) Geometric c) Harmonic

Answer 27

a) Arithmetic No need for calculation since returns are unequal arithmetic will automatically be the largest

Question 28

Which mean is used to annualize multi-period returns? a) Arithmetic b) Geometric c) Harmonic

Answer 28

b) Geometric The geometric mean annualizes returns (e.g., 3-year returns → CAGR).

Question 29

Why can the arithmetic mean mislead investors? a) It ignores compounding b) It’s always lower than the geometric mean c) It excludes outliers

Answer 29

a) It ignores compounding The arithmetic mean overstates growth for volatile returns because it ignores compounding effects.

Question 30

How does dollar-cost averaging use the harmonic mean? a) By buying more shares when prices are low b) By fixing the dollar amount invested c) Both A and B

Answer 30

c) Both A and B Fixed dollar purchases automatically weight cheaper shares more, lowering average cost (harmonic mean < arithmetic mean).

Question 31

Which financial metric is a harmonic mean? a) Price-to-earnings (P/E) ratio average b) Portfolio return c) Sharpe ratio

Answer 31

a) Price-to-earnings (P/E) ratio average The average P/E ratio of a basket of stocks uses the harmonic mean to avoid skew from high P/E outliers.

Question 32

What is the money-weighted rate of return? a) The geometric average of periodic returns b) The IRR of all cash flows in/out of a portfolio c) The return adjusted for inflation

Answer 32

b) The IRR of all cash flows in/out of a portfolio MWR is the IRR that sets the NPV of all cash flows (deposits, withdrawals, beginning/ending values) to zero.

Question 33

Why is TWR preferred for evaluating portfolio managers? a) It reflects the manager’s skill by ignoring cash flow timing b) It accounts for investor contributions/withdrawals c) It always equals the arithmetic mean return

Answer 33

a) It reflects the manager’s skill by ignoring cash flow timing TWR eliminates the impact of cash flow timing, isolating the manager’s performance.

Question 34

How is IRR used in MWR? a) To calculate the average return over multiple periods b) To find the discount rate where NPV of cash flows = 0 c) To adjust returns for risk

Answer 34

b) To find the discount rate where NPV of cash flows = 0

Question 35

If an investor adds funds before poor performance, how does MWR compare to TWR? a) MWR > TWR b) MWR < TWR c) MWR = TWR

Answer 35

b) MWR < TWR Poor performance after deposits lowers MWR (more money was exposed to losses), while TWR is unaffected.

Question 36

When is MWR the appropriate measure? a) For pension funds with regular contributions b) When the manager controls cash flows c) For comparing mutual funds

Answer 36

b) When the manager controls cash flows MWR is suitable when the investor/manager controls timing of cash flows (e.g., private equity).

Question 37

Why do mutual funds report TWR? a) Investors control cash flows b) Managers control cash flows c) To standardize performance comparisons

Answer 37

c) To standardize performance comparisons TWR allows fair comparison across funds, as it’s unaffected by investor deposits/withdrawals.

Question 38

What makes MWR sensitive to timing? a) It compounds returns b) It weights returns by money invested c) It uses geometric mean

Answer 38

b) It weights returns by money invested MWR depends on how much money was exposed to each return period.

Question 39

Why does TWR remove distortions? a) It uses harmonic mean b) It ignores cash flow timing c) It weights returns by time

Answer 39

b) It ignores cash flow timing TWR evaluates only the portfolio’s performance, not when money was added/withdrawn.

Question 40

If an investor adds money before high returns: a) MWR > TWR b) MWR < TWR c) MWR = TWR

Answer 40

a) MWR > TWR More money benefits from high returns → MWR exceeds TWR.

Question 41

When do TWR and MWR give the same result? a) When returns are volatile b) When no cash flows occur c) When using arithmetic mean

Answer 41

b) When no cash flows occur No cash flows → MWR = TWR (no timing impact).

Question 42

Why might MWR misrepresent manager skill? a) It ignores compounding b) It’s distorted by investor cash flows c) It overweights outliers

Answer 42

b) It’s distorted by investor cash flows MWR reflects investor timing, not just manager decisions.

Question 43

How is TWR calculated with cash flows? a) Split into sub-periods at each cash flow b) Use the IRR of all cash flows c) Take the arithmetic mean

Answer 43

a) Split into sub-periods at each cash flow TWR requires valuing the portfolio at each cash flow date to isolate returns.

Question 44

Why do pension funds use TWR? a) They control contribution timing b) They must isolate manager performance c) MWR is too complex

Answer 44

b) They must isolate manager performance Pension sponsors need to evaluate manager skill separately from sponsor contributions.

Question 45

What’s a quick approximation for TWR? a) Arithmetic mean return b) Geometric mean return c) Harmonic mean return

Answer 45

b) Geometric mean return Geometric mean approximates TWR for compound growth.

Question 46

Which return measure aligns with GIPS standards? a) MWR b) TWR c) Arithmetic mean

Answer 46

b) TWR Global Investment Performance Standards (GIPS) mandate TWR for fair comparisons.

Question 47

When dealing with time value of money, what effect does more frequent compounding have on future and present values? a) Increases future value and increases present value b) Decreases future value and increases present value c) Increases future value and decreases present value d) Decreases both future value and present value

Answer 47

c) Increases future value and decreases present value

Question 48

What is the mathematical limit of shortening the compounding period called? a) Instantaneous interest b) Nominal compounding c) Infinite compounding d) Continuous compounding

Answer 48

d) Continuous compounding

Question 49

Which mathematical function is used to convert a holding period return (HPR) into a continuously compounded return? a) Square root b) Natural logarithm (ln) c) Base-10 logarithm (log) d) Exponential function (eⁿ)

Answer 49

c) Base-10 logarithm (log)

Question 50

A key property of continuously compounded returns is that they are: a) Multiplicative over multiple periods b) Additive over multiple periods c) Exponential over multiple periods d) Geometric over multiple periods

Answer 50

b) Additive over multiple periods

Question 51

What does gross return represent? a) Return after fees and costs b) Return before fees for management and administration c) Return after taxes d) Return adjusted for inflation

Answer 51

b) Return before fees for management and administration Gross return measures the total return on an investment before deducting management and administration fees but after necessary trading costs like commissions.

Question 52

Net return is the return: a) Before management fees b) After deducting only taxes c) After deducting management and administration fees d) Before trading commissions

Answer 52

C) After deducting management and administration fees Net return is the return after deducting both trading costs (like commissions) and management and administrative fees.

Question 53

Which costs are deducted in both gross and net returns? a) Management fees b) Commissions and necessary trading costs c) Only tax liabilities d) Only management bonuses

Answer 53

b) Commissions and necessary trading costs Both gross and net returns deduct necessary costs like commissions and trading expenses that are essential to generate returns.

Question 54

Pretax nominal return refers to: a) Return before fees b) Return after paying taxes c) Return before paying taxes d) Return adjusted for inflation

Answer 54

c) Return before paying taxes Pretax nominal return is the return before any taxes are deducted. It reflects the gross earnings from investments.

Question 55

Real return is: a) Nominal return minus taxes b) Nominal return plus inflation c) Nominal return adjusted for inflation d) Nominal return before inflation

Answer 55

c) Nominal return adjusted for inflation Real return adjusts the nominal return by removing the effect of inflation, showing the true increase in purchasing power.

Question 56

If nominal return = 7% and inflation = 2%, the approximate real return is: a) 9% b) 5% c) 4.9% d) 7%

Answer 56

b) 5% Approximate real return = Nominal return − Inflation = 7% − 2% = 5%.

Question 57

The exact real return formula is: a) (1 + Nominal Return) × (1 + Inflation) − 1 b) (1 + Nominal Return) / (1 + Inflation) − 1 c) (Nominal Return + Inflation) / 2 d) Nominal Return − Inflation Rate

Answer 57

b) (1 + Nominal Return) / (1 + Inflation) − 1 Exact real return = [(1 + nominal return) ÷ (1 + inflation)] − 1, accurately adjusting for compounding effects.

Question 58

If inflation is 2% and an investor earns 7%, purchasing power increases approximately: a) 7% b) 5% c) 9% d) 2%

Answer 58

b) 5% 5% is the approximate real return, indicating how much purchasing power has increased.

Question 59

What type of return involves using borrowed funds to magnify gains or losses? a) Net return b) Gross return c) Leveraged return d) Real return

Answer 59

c) Leveraged return Leveraged return arises from using borrowed funds, amplifying both gains and losses relative to the cash invested.

Question 60

Futures contracts typically produce: a) Net returns b) Non-leveraged returns c) Leveraged returns d) Real returns

Answer 60

c) Leveraged returns Futures involve a small margin deposit to control a much larger value, creating leverage.

Question 61

Leveraged investments are common in which asset class? a) Real estate b) Bonds c) Mutual funds d) ETFs

Answer 61

a) Real estate Real estate investors commonly finance a property partially with debt, creating leverage.

Question 62

A fund’s unleveraged return (money amount) is calculated as: a) r × (V0 + VB) b) r × V0 c) (r − rB) × VB d) rB × VB

Answer 62

b) r × V0 Without leverage, the return is simply the rate earned (r) multiplied by the initial value (V0).

Question 63

In the leveraged return formula, rB represents: a) Rate of return on the asset b) Risk-free rate c) Borrowing interest rate d) Benchmark return

Answer 63

c) Borrowing interest rate rB is the interest rate paid on borrowed funds, reducing the gross leveraged return.