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rate of returns Flashcards

chp 1 rates and returns (128 cards)

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1
Q

What are the three interpretations of an interest rate?

A
  1. Required rate of return
  2. Discount rate
  3. Opportunity cost

Interest rates reflect the relationship between differently dated cash flows.

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2
Q

What components make up an interest rate?

A
  1. Real risk-free interest rate
  2. Inflation premium
  3. Default risk premium
  4. Liquidity premium
  5. Maturity premium

These premiums compensate lenders for bearing distinct types of risk.

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3
Q

Define the nominal risk-free interest rate.

A

The sum of the real risk-free interest rate and the inflation premium.

It reflects the combination of the real risk-free rate plus compensation for expected inflation.

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4
Q

What is the difference between gross return and net return?

A

Gross return is the return prior to deduction of managerial and administrative expenses. Net return is gross return minus these expenses.

Net return is a better measure of what an investor actually earned.

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5
Q

What is a holding period return (R)?

A

The return that an investor earns for a single specified period of time.

Examples include one day, one month, or five years.

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6
Q

What is the difference between money-weighted and time-weighted returns?

A

Money-weighted return accounts for the value and timing of cash flows. Time-weighted return measures the compound rate of growth of one unit of currency invested.

Time-weighted return is preferred for evaluating portfolio managers.

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7
Q

What does annualizing periodic returns allow investors to do?

A

It allows investors to compare different investments across different holding periods.

This helps in evaluating and comparing relative performance.

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8
Q

Fill in the blank: The real risk-free interest rate reflects the __________ of individuals for current versus future real consumption.

A

time preferences

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9
Q

True or False: The liquidity premium compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly.

A

True

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10
Q

What is the formula for calculating an interest rate (r)?

A

r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium

This formula shows how different components contribute to the overall interest rate.

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11
Q

What is the primary reason for the existence of a default risk premium?

A

To compensate investors for the possibility that the borrower will fail to make a promised payment.

This premium reflects the risk associated with the borrower’s creditworthiness.

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12
Q

Describe the term ‘after-tax nominal return’.

A

Total return minus any allowance for taxes on dividends, interest, and realized gains.

This measure provides a clearer picture of actual earnings after tax implications.

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13
Q

What are the two types of return generated by financial assets?

A
  1. Periodic income through cash dividends or interest payments
  2. Capital gain or loss from changes in the price of the financial asset

Some financial assets may provide return through only one of these mechanisms.

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14
Q

What does the term ‘leveraging a portfolio’ refer to?

A

Using borrowing or futures to amplify the portfolio’s gains or losses.

Leverage can increase both potential returns and risks.

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15
Q

What is the significance of using different return measures like arithmetic mean or geometric mean?

A

They have special applications for evaluating investments depending on the presence of outliers and compounding.

The choice of mean affects the interpretation of investment performance.

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16
Q

Estimate the default risk premium affecting all securities if Investment 4 has an interest rate of 4.0% and Investment 5 has an interest rate of 6.5%.

A

2.0 percent

This is calculated after accounting for a liquidity premium of 0.5 percent.

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17
Q

What is the expected interest rate range for Investment 3 based on its risk profile?

A

Between 2.5 percent and 4.5 percent

This range considers its liquidity and maturity risks compared to other investments.

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18
Q

What are the two primary ways financial assets provide returns?

A

Through cash dividends or interest payments and price movement.

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19
Q

What is a holding period return (R)?

A

The return earned from holding an asset for a single specified period of time.

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20
Q

How is holding period return calculated when an asset is purchased at 100 and sold at 105 with no dividends?

A

R = (105 - 100) / 100 = 5 percent.

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21
Q

If an asset also pays income of two units at the end of the period, what is the total return?

A

Total return = 7 percent.

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22
Q

How can returns be expressed?

A

In decimals (0.07), fractions (7/100), or as a percent (7 percent).

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23
Q

What is the formula for computing one-year holding period return from multiple annual returns?

A

R = [(1 + R1) x (1 + R2) x (1 + R3)] - 1.

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24
Q

What is the simplest way to compute a summary measure for returns across multiple periods?

A

Take a simple arithmetic average of the holding period returns.

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25
How is the arithmetic mean return denoted?
Ri.
26
What is the formula for arithmetic mean return?
Rt = (R1 + R2 + ... + Rn) / T.
27
What does the geometric mean return account for?
The compounding of returns.
28
What is the formula for geometric mean return?
RGi = [(1 + R1) x (1 + R2) x ... x (1 + RT)]^(1/T) - 1.
29
What is the difference between arithmetic mean and geometric mean returns?
Arithmetic mean is biased upward, while geometric mean accounts for compounding.
30
True or False: The geometric mean return can be greater than the arithmetic mean return.
False.
31
In the holding period return example, what was the calculated return if the investor sold shares for USD30.50 with a dividend payment of USD51.55?
-10.1 percent.
32
What is the holding period return for a mutual fund with annual returns of 14%, -10%, and -2%?
0.55 percent.
33
What is the geometric mean return for a hedge fund with annual returns of 22%, -25%, and 11%?
0.52 percent.
34
How does variability in returns affect the difference between arithmetic and geometric means?
The difference increases with variability; more dispersed observations lead to a greater difference.
35
Fill in the blank: The geometric mean return represents the _______ rate of return on an investment.
growth.
36
What happens to the geometric mean when all observations in a series are the same?
The geometric mean equals the arithmetic mean.
37
What is the impact of using arithmetic mean on historical performance assessment?
It can distort the assessment.
38
What is the ending amount of an investment of EUR100 after two years if it was worth EUR100 at the beginning and EUR200 in between?
EUR100.
39
What is the geometric mean of O percent?
The compound rate of growth during two years is 0%.
40
How is the arithmetic mean calculated?
Arithmetic mean = [100% + -50%]/2 = 25%.
41
When should the arithmetic mean be used?
To estimate the average return over a one-period horizon.
42
When should the geometric mean be used?
To estimate the average returns over more than one period.
43
What is the harmonic mean appropriate for?
It is appropriate when the variable is a rate or a ratio.
44
What is the formula for the harmonic mean?
Harmonic mean = n / (Σ(1/Xi)), where Xi > 0.
45
What is the effect of outliers on the harmonic mean?
The harmonic mean is less influenced by outliers compared to the arithmetic mean.
46
Calculate the harmonic mean of the prices EUR10 and EUR15.
Harmonic mean = 2/[(1/10) + (1/15)] = EUR12.
47
What is the relationship between arithmetic, geometric, and harmonic means?
Arithmetic mean x Harmonic mean = (Geometric mean)².
48
Is the harmonic mean always less than the geometric mean?
Yes, unless all observations are the same.
49
What is the equation for calculating the internal rate of return (IRR)?
Σ(CF_t / (1 + IRR)^t) = 0.
50
What does the money-weighted return account for?
The money invested and the actual return earned on investment.
51
What is the formula for the cash flows in the IRR calculation?
CF0 = -100, CF1 = -950, CF2 = +350, CF3 = +1,270.
52
What is the investor's internal rate of return (IRR) in the provided example?
IRR = 26.11%.
53
What Excel function can be used to calculate the IRR?
=IRR(values).
54
What does the harmonic mean minimize?
The impact of outliers in a dataset.
55
What is a trimmed mean?
A mean calculated after removing a small defined percentage of extreme values.
56
What is a winsorized mean?
A mean calculated after replacing extreme values with their nearest observations.
57
What factors influence the choice of mean to use?
* Presence of outliers * Symmetry of the distribution * Compounding * Presence of extreme outliers.
58
What is the average price paid per share in the cost averaging example?
EUR12.
59
What is the arithmetic mean P/E for the 10 stocks?
Arithmetic mean = 121.48/10 = 12.148.
60
What is the geometric mean P/E for the 10 stocks?
Geometric mean = 11.4287.
61
What is the harmonic mean P/E for the 10 stocks?
Harmonic mean = 10.8142.
62
What is the impact of a negative return on a larger investment?
It significantly hurts the total return.
63
What does the money-weighted return tell an investor?
What she earned on the actual euros invested for the entire period.
64
What is the money-weighted rate of return calculated in the example?
9.39 percent ## Footnote The money-weighted return accounts for the timing and amount of cash flows.
65
What were the cash outflows for the investment at time t = 0?
-USD200 ## Footnote This represents the cost to purchase the first share.
66
What were the cash inflows at time t = 1?
USD5 from the first share and USD10 from the second share ## Footnote The USD10 is derived from the USD5 dividend per share for two shares.
67
What is the holding period return for the first year?
15% ## Footnote Calculated as (USD5 + USD225 - USD200) / USD200.
68
What is the holding period return for the second year?
6.67% ## Footnote Calculated as (USD10 + USD470 - USD450) / USD450.
69
What is the mean holding period return for the two years?
10.84% ## Footnote This is the average of the first and second-year returns.
70
True or False: The money-weighted return allows for comparison between different investors.
False ## Footnote It does not allow for comparison as different investors may have different cash flows.
71
What is the holding period return formula used to calculate the five-year holding period return?
R = (1 + R1)(1 + R2)(1 + R3)(1 + R4)(1 + R5) - 1 ## Footnote This formula compounds the returns over the years.
72
What is the arithmetic mean annual return for the Rhein Valley Superior Fund?
7.60% ## Footnote Calculated as the average of the annual returns over five years.
73
What is the geometric mean annual return for the Rhein Valley Superior Fund?
7.32% ## Footnote This is slightly less than the arithmetic mean return.
74
What is the calculated money-weighted rate of return for the Lohrmanns' investment?
5.86 percent ## Footnote This is determined by evaluating the present value of cash flows.
75
What is the definition of the time-weighted rate of return?
An investment measure that is not sensitive to the additions and withdrawals of funds ## Footnote It measures the compound rate of growth of an initial investment.
76
What are the three steps to compute an exact time-weighted rate of return?
* Price the portfolio before cash flows * Calculate holding period returns for each subperiod * Link holding period returns to obtain an annual rate ## Footnote This method helps neutralize the impact of cash flows on performance measurement.
77
What is the time-weighted return calculated for the portfolio in the example?
10.76% ## Footnote This is derived from the geometric mean of the two holding period returns.
78
How is the annualized time-weighted return calculated?
As the geometric mean of N annual returns ## Footnote This allows for a more consistent measure of performance across multiple years.
79
What is the significance of frequent portfolio valuations in time-weighted returns?
More frequent valuations lead to more accurate approximations ## Footnote Daily valuations can provide precise time-weighted rates of return.
80
What was the ending value of the in-house account at the end of Quarter 4?
USD5,508,000 ## Footnote This is the value after accounting for inflows and outflows during the quarter.
81
What was the beginning value of the Super Trust Account in Quarter 1?
USD10,000,000 ## Footnote This represents the starting investment before any cash flows.
82
What is the formula for calculating the time-weighted rate of return (RTw)?
RTw = (1 + r1)(1 + r2)(1 + r3)(1 + r4) - 1
83
What is the time-weighted rate of return for the Super Trust account?
26.02 percent
84
How is the first quarter holding period return (HPR) calculated for the Super Trust account?
r1 = (USD13,200,000 - USD12,000,000) / USD12,000,000 = 0.10
85
What is the formula for the money-weighted rate of return?
It requires finding the discount rate that sets the sum of the present value of cash inflows and outflows equal to zero.
86
What is the four-month holding period return (R) for the Walbright Fund from January to May?
R = USD110 million / USD100 million = 1.12 or 12%
87
What is the time-weighted rate of return for the Walbright Fund?
21.03 percent
88
What does the money-weighted return reflect in terms of fund performance?
It is sensitive to the timing and amount of withdrawals and additions to the portfolio.
89
Fill in the blank: The annualized return for a weekly return of 0.2 percent is _______.
10.95 percent
90
What is the present value formula for non-annual compounding?
PV = FVN / (1 + R/m)^(mN)
91
What is the required present value for investing in a GIC to grow to CAD5 million at 6 percent interest compounded monthly?
CAD 2,748,163.67
92
True or False: The time-weighted return is always greater than the money-weighted return.
False
93
What is the impact of rounding on the performance difference between two portfolios?
It may seem trivial, yet it can be substantive on a large portfolio.
94
What is the annualized return for an 18-month holding period return of 20 percent?
12.92 percent
95
How do you annualize a return for a period longer than one year?
Use Rannual = (1 + Rholding period)^(c) - 1, where c is the number of holding periods in a year.
96
What is the significance of the cash flows on 1 May for the Walbright Fund?
They include a cash inflow of USD2 million and cash outflows of USD22 million.
97
How is the cash flow at the end of the third four-month interval represented?
CF3 = 142.64 million (includes dividends and terminal market value)
98
What is the annualized return for a 15-day holding period return of 0.4 percent?
10.20 percent
99
What is the key limitation of annualizing returns?
It assumes returns can be repeated precisely.
100
What does the term 'holding period return' (HPR) refer to?
The return generated over a specific period of time.
101
What is the market value of the Walbright Fund on 31 December, excluding dividends?
USD 140 million
102
What is a major limitation of annualizing returns?
The implicit assumption that returns can be repeated precisely and reinvested while earning a similar return. ## Footnote This assumption does not always hold true in real market conditions.
103
What is the annualized return for Security A if it earned 6.2% over 100 days?
24.55% ## Footnote Calculated using the formula RsA= (1 + 0.062)^(365/100) - 1.
104
Which security generated the highest annualized return among Security A, B, and C?
Security B with an annualized return of 29.36%. ## Footnote Security B's return is calculated over 4 weeks.
105
What is the annualized return for ETF 1 if it has a return of 4.61% over 146 days?
11.93% ## Footnote Calculated using the formula for annualized return.
106
True or False: ETF 2 has the highest annualized rate of return despite having the lowest periodic return.
True ## Footnote This is due to the effects of reinvestment and compounding.
107
What is the formula for continuously compounded return?
ln(Ending Price / Beginning Price) ## Footnote This can also be expressed as ln(1 + Holding Period Return).
108
If an asset's value increases from USD 30 to USD 34.50, what is the continuously compounded return?
13.98% ## Footnote This is calculated as ln(34.50/30).
109
What is the relationship between nominal returns and real returns?
Nominal return = Real return + Inflation premium + Risk premium ## Footnote This relationship helps in understanding the effect of inflation on returns.
110
What does gross return represent?
The return earned by an asset manager before deductions for management expenses, taxes, and other fees. ## Footnote It reflects the actual performance of the asset manager's investment skill.
111
What is net return?
The return after deducting all managerial and administrative expenses. ## Footnote It represents what the investor actually receives.
112
Fill in the blank: After-tax nominal return is computed as the total return minus any allowance for _______.
taxes on dividends, interest, and realized gains.
113
What is the after-tax real return?
The return received after accounting for taxes and inflation. ## Footnote It serves as a reliable benchmark for making investment decisions.
114
What is a leveraged return?
The return on an investment that exceeds the investment of one's own money, achieved by borrowing funds. ## Footnote Leverage amplifies both gains and losses.
115
What happens to the leveraged return if the total investment return is less than the borrowing cost?
Leverage decreases the leveraged return (RL). ## Footnote This highlights the risks associated with using leverage.
116
What is the formula for calculating the leveraged return?
RL = Rp + (Rp - rv) ## Footnote Where Rp is the portfolio return and rv is the cost of borrowed funds.
117
What is the formula for leveraged return (RL)?
RL = RP + (Rp - rv) ## Footnote Where RP is the total investment return, Rp is the return on the portfolio, and rv is the cost of debt.
118
If Rp < r0, what happens to leverage?
Leverage decreases RL ## Footnote This indicates that if the return on the portfolio is less than the cost of debt, the overall leveraged return is reduced.
119
In the example given, what is the total investment return (Rp) for the EUR10 million equity portfolio?
8 percent ## Footnote The total investment return is given as 8 percent for the portfolio.
120
If a portfolio is financed 30 percent with debt at 5 percent, what is the leveraged return (RL) calculated in the example?
9.29 percent ## Footnote The leveraged return is derived from the calculation involving the portfolio return and the cost of debt.
121
What is the geometric return for equities according to the historic asset class returns?
8.0 percent ## Footnote This value represents the average compounded return for equities over a specified period.
122
What is the geometric return for corporate bonds?
6.5 percent ## Footnote This indicates the compounded average return for corporate bonds.
123
What is the geometric return for treasury bills?
2.5 percent ## Footnote This reflects the average return on treasury bills.
124
What is the geometric return for inflation?
2.1 percent ## Footnote This represents the average inflation rate over the given period.
125
What is the closest real rate of return for equities?
5.8 percent ## Footnote This is calculated using the formula: (1 + 0.080)/(1 + 0.0210) - 1.
126
What is the closest real rate of return for corporate bonds?
4.3 percent ## Footnote This is derived from the formula: (1 + 0.065)/(1 + 0.0210) - 1.
127
What is the risk premium for equities?
5.4 percent ## Footnote Calculated as: (1 + 0.080)/(1 + 0.0250) - 1.
128
What is the risk premium for corporate bonds?
3.9 percent ## Footnote This is calculated using: (1 + 0.0650)/(1 + 0.0250) - 1.

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