Performance Questions Flashcards
One method for evaluating the performance of a portfolio is the time-weighted rate of
return. The time-weighted rate of return is also the geometric mean rate of return (GMR).
Calculate the GMR/TWRR of the following:
Year 1: 30%
Year 2: 20%
Year 3: 10%
Year 4: 0%
Steps:
1) The questions gave us the PPRs
2) convert the PPRRs by adding 1
(1.3, 1.2, 1.1, 1.0)
3) Then multiply the PPRRs together to get an HPRR, and
then take the nth root.
(1.3, 1.2, 1.1, 1.0) 1/4 -1 = 0.1445 or 14.45%
use the Yx button on calculator to take the nth
cash flow is not taken into consideration
The other method for evaluating the performance of a portfolio is known as the dollar-weighted rate of return. This is measured with a value known as an internal rate of return. This method is also used when we want to take into consideration cash inflows and outflows.
Calculate the IRR/DWRR for the following:
Portfolio A:
PV: $1,000
Deposits: $1,000 (yr 2), $1,000 (yr 3), $1,000 (yr 4)
Return: 1.3% (yr 1), 1.2% (yr 2), 1.1% (yr 3), 1.0% (yr 4)
Portfolio B:
PV: $1,000
Deposits: $1,000 (yr 2), $1,000 (yr 3), $1,000 (yr 4)
Return: 1.0% (yr 1), 1.1% (yr 2), 1.2% (yr 3), 1.3% (yr 4)
Portfolio A:
FV Calc: $1,000 x 1.3% + $1,000 x 1.2% + $1,000 x 1.1% +$1,000 x 1% = $5,136
SHIFT, C ALL
1000, +/–, CFj
1000, +/–, CFj
1000, +/–, CFj
1000, +/–, CFj
5136, CFj
SHIFT, IRR/YR
{Display: 10.25[%]}
Portfolio B:
FV Calc: $1,000 x 1.0% + $1,000 x 1.1% + $1,000 x 1.2% +$1,000 x 1.3% = $6,292
SHIFT, C ALL
1000, +/–, CFj
1000, +/–, CFj
1000, +/–, CFj
1000, +/–, CFj
6292, CFj
SHIFT, IRR/YR
{Display: 18.97[%]}
Compute the arithmetic mean return and geometric mean return for an investment
with the following returns over the last 3 years: –22 percent, 7 percent, and 21 percent.
The arithmetic mean return is computed by summing the rates of return for time periods 1 through T, and dividing this total by the number of time periods (T).
For the arithmetic mean return: (–22% + 7% + 21%)/3 = 2%.
For the geometric mean
return, we must begin by computing the PPRRs as follows: PPRR1
= 1 – .22 = .78, PPRR2
= 1 + .07 = 1.07, and PPRR3
= 1 + .21 = 1.21. Next, we compute the HPRR as: HPRR =
(0.78)(1.07)(1.21) = 1.0099. Then we can compute the geometric mean return by taking
the cube root of the HPRR (it is the cube root because there are three time periods),
and subtracting one, as follows:
GMR = (HPRR)1/n – 1 = GMR = 1.00991/3 – 1= 1.0033 – 1 = .0033, or .33 percent.
HP-10BII keystrokes: SHIFT, C ALL; .78, x, 1.07, x, 1.21, =; SHIFT, yx
, .3333, =; –, 1, =;
{Display: 0.0033}
although the most fundamental measurement of risk is variance, the most commonly used measurement is the standard deviation, which is the square root of the
variance.
You note that the returns on a stock for the last 3 years are –15 percent, 5 percent, and 28 percent. You believe these returns are representative of future returns, and you are willing to base your estimate of expected return and standard deviation on these historical data. The expected return and standard deviation are computed as:
SHIFT, C ALL
15, +/–, Σ+
5, Σ+
28, Σ+
SHIFT, x,y – – {Display: 6.00}
SHIFT, sx, sy
{Display: 21.52}
Note that the x,y – – key is the “7” key and the sx, sy
key is the “8” key.
Assume XYZ stock has the following rates of return for the last 3 years: –15 percent, 10 percent, and 35 percent. Determine XYZ’s arithmetic mean return and standard deviation based on this historical data.
Arithmetic Mean Return = (–15% + 10% + 35%)/3 = 10%
Standard Deviation:
Keystrokes:
SHIFT, C ALL;
15, +/–, Σ +; 10, Σ +; 35, Σ +;
SHIFT, x,y,
SHIFT, Sx, Sy
{Display: 25}
As you review a new client’s brokerage statement, you notice that there are a lot of trades over the last 3 months. You decide to compute the portfolio turnover
ratio. The value of the account at the start of the 3-month period is $517,850, and it is $485,219 at the end. The sums of all purchases and sales, excluding bonds
maturing, are $65,270 and $57,977, respectively. The 3-month portfolio turnover ratio (PTR) is?
3-month PTR = $57,977 ÷ [($517,850 + $485,219) ÷ 2] = .1156
Annualized, this ratio is .4624 (.1156 × 4), which means that 46.24 percent of this portfolio is being turned at an annual rate. This is not an unreasonable turnover
ratio, especially if this is an actively managed portfolio and there are some good reasons for these trades.
Portfolio turnover ration = lesser of purchases or sales / avg account value
A company just paid a dividend of $1 per share. If the stock price is $21 and the expected growth rate of dividends is 7 percent, what is the expected rate of return for this stock? (A) 9.50 percent (B) 10.00 percent (C) 11.76 percent (D) 12.10 percent
The answer is (D).
The formula for the expected rate of return is r = D1/P0 + g. The question gives the value of D0. To convert this to D1, multiply D0 by (1 + g): D1 = $1 x (1 + .07) = $1.07. This value is then plugged into the numerator, and the price of $21 is inserted into the denominator, along with the value of .07 for the growth rate. The solution is: r = [1.07/21] + .07 = .1210 or 12.10%.
Fiscal =
Monetary =
Fiscal = Congress Monetary = Fed
A mutual fund has 10 million shares outstanding, a portfolio with a market value of $201 million, liabilities of $1 million, and a 5 percent load. What would be the total cost to an investor buying 100 shares? (A) $2,100.00 (B) $2,105.26 (C) $2,110.11 (D) $2,115.79
The answer is (B).
The NAV is computed as the market value of the portfolio minus any liabilities of the fund then divided by the number of shares outstanding, which in this case equals $20.00. The price per share paid by the investor is the NAV divided by one minus the load (in decimal form), or $20.00/(1 – .05) = $21.0526. This is then multiplied by 100 shares for a total price of $2,105.26.
nonqualified dividends vs qualified dividends
nonqualified dividends are taxed at ordinary income rates, while qualified dividends receive more favorable tax treatment by being taxed at capital gains rates.
Over the last 3 years, a stock has achieved rates of return of -10 percent, 0 percent, and 10 percent. Which of the following statements is (are) correct with regard to the standard deviation and variance of these returns?
I. The standard deviation is 7.78 percent.
II. The variance is 100 percent-squared.
The answer is (B).
I is incorrect. The mean return is 0 percent ([10% + 0% –10%]/3). The variance is [(–10% – 0%)2 + (0% – 0%)2 + (10% – 0%)2]/(3 – 1) = 100 percent-squared. The standard deviation is the square root of this, or 10 percent. Keystrokes for the standard deviation: Shift, C ALL; 10, +/-, ∑+; 0, ∑+; 10, ∑+; Shift, SxSy. Keystrokes for variance: Shift, x2.
14, 2, 12, –10, and –3.
Arithmetic mean?
Standard deviation?
Variance?
Arithmetic mean: 14, ∑+, +, 2, ∑+, +, 12, ∑+, +, 10, +/-, ∑+, +, 3, +/-, ∑+, +, SHIFT, ( x,y) {Display: 3.0000}
Standard Deviation: 14, ∑+, +, 2, ∑+, +, 12, ∑+, +, 10, +/-, ∑+, +, 3, +/-, ∑+, +, SHIFT, (Sx,Sy) {Display: 10.0995}
Variance:
First calculate the standard deviation: 14, ∑+, +, 2, ∑+, +, 12, ∑+, +, 10, +/-, ∑+, +, 3, +/-, ∑+, +, SHIFT, (Sx,Sy) {Display: 10.0995}
SHIFT, (X2 (the plus sign))
At time zero, a portfolio is worth $10,000. At the end of the first period, $5,000 is added to the portfolio, after which the portfolio is worth $16,000. At the end of the second period, the portfolio is worth $20,000.
I. The time-weighted rate of return is
II. The dollar-weighted rate of return is
Time Weighted Rate of Return
The first period’s return relative is 1.10, as it is measured before the addition of the $5,000 ($11,000/$10,000). The second period’s return relative is 1.25 ($20,000/$16,000). The time-weighted rate of return is the square root of the product of these two return relatives minus 1, or 17.26 percent. The keystrokes for the time-weighted rate of return are: SHIFT, C ALL, 1.1, x, 1.25, =, SHIFT, yx, .5, =, –, 1, = {Display: .1726}.
Dollar Weighted Rate of Return
The keystrokes for the dollar-weighted rate of return are: SHIFT, C ALL, 10000, +/-, CFj, 5000, +/-, CFj, 20000, CFj, SHIFT, IRR/YR (display: 18.61).
Your portfolio has an initial value of $10,000. At the end of the first year, it is worth $13,000. At the end of the second year, you draw out $2,000, and after the draw it is worth $10,000 again.
I. The time-weighted rate of return is
II. The dollar-weighted rate of return is
Time Weighted Rate of Return
To compute the time-weighted rate of return, we need to first compute the PPR for each eriod. For period one, it is +30%. For period two, we first have to add back the $2,000 withdrawal, to obtain a rate of return of -7.69% [(12,000/13,000) – 1]. The computation is then: (1.30 x .9231).5 – 1 = .0955 or 9.55%.
Dollar Weighted Rate of Return
To compute the dollar-weighted rate of return, we can ignore the $2,000 withdrawal as it is still part of the portfolio ending value of $12,000. The cash flow numbers are: –10,000, 0, and +12,000. The keystrokes are: SHIFT, C ALL; 10000, +/- CFj; 0, CFj; 12000, CFj; SHIFT, IRR/YR {Display: 9.54}.
Which of the following statements regarding annualized rates of return is (are) correct?
I. If you earn 16 percent during an 18-month period, then your annualized rate of return over this same time period is 10.4 percent.
II. If you earn 8 percent during a 6-month period, then your annualized rate of return over this same time period is 16 percent.
I only
To annualize the 16% rate of return, the computation is: (1 + .16)12/18 – 1 = .10140. The keystrokes are: SHIFT C ALL; 1, + .16, SHIFT, yx, .6667, =, –, 1, = {Display: .1040}.
II is incorrect because the computation is: (1 + .08)2 – 1 = .1664. The keystrokes are: SHIFT, C ALL; 1, +, .08, =, SHIFT, yx, 2, =, –1, = {Display: .1664}.
