CFA 2 - Quantitative Methods - 1.1 TV of Money

Question 1

What does the time value of money quantify?

Answer 1

The relationship between cash flows that occur on different dates.

Question 2

Which amount is preferable: $100 today or $105 today?

Answer 2

$105 today.

Question 3

To compare $100 today and $105 in one year, what must be converted?

Answer 3

The future cash flow into its present equivalent.

Question 4

What is needed to convert future cash flows into present value?

Answer 4

An interest rate, also known as a yield.

Question 5

What is a required rate of return?

Answer 5

The rate an investor requires when lending money, e.g., 5% for $100 to $105.

Question 6

Define discount rate in the context of the time value of money.

Answer 6

A rate used to convert future cash flows into present value.

Question 7

If a 5% discount rate is used, what is $105 in one year equivalent to today?

Answer 7

$100 today.

Question 8

What does opportunity cost refer to in financial decisions?

Answer 8

The loss of potential gain from other investments when spending money.

Question 9

Fill in the blank: The decision to spend $100 today means giving up the opportunity to invest and have it grow to _______ over the next year.

Answer 9

$105.

Question 10

What determines interest rates?

Answer 10

The interaction between the forces of supply and demand

Question 11

Who supplies funds in financial markets?

Answer 11

Savers who prefer a higher rate of return

Question 12

Who demands funds in financial markets?

Answer 12

Borrowers who want to pay a lower interest rate

Question 13

What is the equilibrium interest rate?

Answer 13

The rate that emerges from the collective interactions between borrowers and savers

Question 14

Is there a single interest rate used for all loans?

Answer 14

No

Question 15

What formula is used to calculate the required interest rate, r?

Answer 15

r = rf + I + D + L + M

Question 16

What does ‘rf’ represent in the interest rate formula?

Answer 16

The real risk-free rate

Question 17

What is the real risk-free rate?

Answer 17

Compensation for a risk-free loan with no expected inflation

Question 18

What does ‘I’ stand for in the interest rate formula?

Answer 18

The inflation premium

Question 19

What is the purpose of the inflation premium?

Answer 19

To compensate lenders for expected inflation

Question 20

What does ‘D’ represent in the interest rate formula?

Answer 20

The default risk premium

Question 21

What is the default risk premium?

Answer 21

The charge for the possibility that borrowers will not meet their obligations

Question 22

What does ‘L’ stand for in the interest rate formula?

Answer 22

The liquidity premium

Question 23

What is the liquidity premium?

Answer 23

Compensation for the extra cost of converting an investment to cash quickly

Question 24

What does ‘M’ represent in the interest rate formula?

Answer 24

The maturity premium

Question 25

What is the maturity premium?

Answer 25

Compensation for lending over longer periods with greater exposure to interest rate risk

Question 26

Why are government securities referred to as 'risk-free'?

Answer 26

They carry no default risk

Question 27

Do government securities typically carry a liquidity premium?

Answer 27

Little-to-no liquidity premium

Question 28

Why do yields on corporate debt reflect a liquidity premium?

Answer 28

Investors are more likely to accept a discount to market value when selling their positions

Question 29

True or False: Longer-dated government bonds have yields that reflect a maturity premium.

Answer 29

True

Question 30

Fill in the blank: The required interest rate, r, can be calculated by adding the real risk-free rate and the _______.

Answer 30

[inflation premium, default risk premium, liquidity premium, maturity premium]

Question 31

What does the nominal risk-free rate reflect?

Answer 31

The real risk-free rate and the premium for expected inflation ## Footnote The nominal risk-free rate is an important concept in finance, indicating the return on an investment with no risk of financial loss.

Question 32

What formula should be used to calculate the nominal risk-free rate over more than one period?

Answer 32

A multiplicative formula ## Footnote This approach captures the impact of compounding over multiple periods.

Question 33

Fill in the blank: (1 + Nominal risk-free rate) = (1 + _______) * (1 + inflation premium)

Answer 33

real risk-free rate

Question 34

What is the relationship between the nominal risk-free rate, real risk-free rate, and inflation premium?

Answer 34

Nominal risk-free rate = (1 + real risk-free rate) * (1 + inflation premium) ## Footnote This equation shows how inflation affects the nominal rate of return.

Question 35

What are the two components of returns on financial assets?

Answer 35

Capital appreciation and income ## Footnote Capital appreciation refers to the change in the asset’s value, while income includes periodic cash flows like coupon or dividend payments.

Question 36

What are capital gains based on?

Answer 36

The change in the asset’s value over the investor’s holding period ## Footnote Capital gains can be positive (gains) or negative (losses).

Question 37

What does the income component of returns include?

Answer 37

Periodic cash flows such as coupon payments on bonds or dividend payments made by stocks ## Footnote Income is an important part of total returns for many investments.

Question 38

What is the return on a non-dividend-paying stock or a zero-coupon bond attributed to?

Answer 38

Capital appreciation ## Footnote These investments do not provide periodic income.

Question 39

What is a holding period return (HPR)?

Answer 39

The rate of return for the single period from when the investment is made to when the position is sold ## Footnote The holding period can vary in length.

Question 40

Why is it necessary to use a common reference period for return measures?

Answer 40

To compare returns on investments held for different lengths of time ## Footnote This allows for fair comparisons across various investments.

Question 41

How can returns on investments held for different periods be compared?

Answer 41

By calculating their mean annual returns ## Footnote This method standardizes the comparison over a common timeframe.

Question 42

What is the arithmetic mean return?

Answer 42

The simple average of returns over multiple periods ## Footnote It is calculated by summing all returns and dividing by the number of periods.

Question 43

Fill in the blank: The arithmetic mean return is calculated by summing all returns and dividing by the number of _______.

Answer 43

Periods ## Footnote This provides an average return per time unit.

Question 44

What is the geometric mean used for?

Answer 44

To average rates over time or compute growth rates ## Footnote It is often used to average portfolio returns from different time periods.

Question 45

What must be done to each return when calculating a geometric mean rate of return?

Answer 45

One must be added to each return expressed in decimal form.

Question 46

What does the geometric mean return represent?

Answer 46

An investment's compound growth rate over multiple periods.

Question 47

When is the arithmetic mean used?

Answer 47

To measure performance for a single period.

Question 48

How does the geometric mean reflect compounding?

Answer 48

It shows how the total returns are linked over time.

Question 49

Is the geometric mean typically greater than or less than the arithmetic mean?

Answer 49

Less than the portfolio's arithmetic mean return.

Question 50

When will the geometric mean and arithmetic mean be equal?

Answer 50

When all observations have the same value.

Question 51

What happens to the difference between the geometric mean and arithmetic mean with greater dispersion among observations?

Answer 51

The difference increases.

Question 52

What effect does greater variability among observations have on the arithmetic mean?

Answer 52

It increases the upward bias.

Question 53

How is the upward bias of the arithmetic mean particularly evident?

Answer 53

When the data series includes both positive and negative returns.

Question 54

The harmonic mean

Answer 54

calculated as the reciprocal of the average of the reciprocals for all observations To calculate a harmonic mean rate of return, the inputs must be adjusted like they are when calculating the geometric mean return

Question 55

Compared to arithmetic and geometric means, the harmonic mean is not as commonly used in practice. However, it is appropriate for some circumstances. Importantly, compared to these other measures of returns, the harmonic mean is less influenced by extreme values, known as outliers, because...

Answer 55

each observation's weight is inversely proportional to its magnitude.

Question 56

when is the harmonic mean useful

Answer 56

The harmonic mean is useful when summarizing data in ratio form (e.g., P/Es). It is also appropriate for finding the average price paid for a security when the price changes but the amount invested remains constant for each purchase. --> This is known as the cost averaging technique

Question 57

Unless all observations in a data series have the same value, the harmonic mean is always less than the geometric mean, which is less than the arithmetic mean true or false

Answer 57

true

Question 58

The relationship between the Arithmetic Mean, Harmonic mean, and geometric mean can be measured using which formula

Answer 58

Arithmetic Mean * Harmonic Mean = Geometric Mean ^ 2

Question 59

A trimmed mean

Answer 59

calculated by discarding a certain percentage of the highest and lowest values. For example, with a sample of 100 observations, a 2% trimmed mean would be the arithmetic mean without the highest value (top 1%) and the lowest value (bottom 1%).