Unit 23 summed
An investor purchased stock for $50 per share at the beginning of the year. In December, the investor liquidated his stock for $55 per share, while also receiving dividends of $2 per share during the year. Assuming an inflation rate of 3%, what is the investor's real rate of return?
11% Given the fact the client liquidated his shares at a price of $55, we can conclude that he attained a 10% ($5 profit ÷ $50 initial investment) return based on capital appreciation of the stock. He also received dividends of $2 per share giving him an additional return of 4% ($2 ÷ $50). By adding these 2 percentages together, we can conclude that his total return is 14%, less an inflation rate of 3%, which would give a real rate of return of 11%.
he Sharpe ratio measures the risk-adjusted return. A higher Sharpe ratio indicates that, based on the risk taken, the investor's return is better than expected.
6000 440
To our knowledge, the exam has never asked a question this complicated. But, things can always change so we wanted you to get the "flavor" of combining probable return (which is tested) with hedge fund performance fees. With a 30% gain, the fund would earn fees of 2% + 0.20(30% - 2%) = 2% + 0.20 (28%) = 2% + 5.6% = 7.6%. With a 10% loss, the fund would only earn its management fee of 2%. To the investor, the expected return is 0.5(-10% - 2%) = 0.5 (-12%) = -6% + 0.5(30% - 7.6%) = -6% + 0.5 (22.4%) = -6% + 11.2% = 5.2%.
A hedge fund with a 2-plus-20% fee structure has equal probabilities of a 10% loss or a 30% gain in its first year. The probable return to an investor in the fund for the first year is closest to A) 17.6%. B) 5.2%. C) -2.0%. D) 8.8%.
The formula for the Sharpe ratio is: actual return minus the risk-free rate which is then divided by the standard deviation.
An analyst computing a stock's Sharpe ratio would need to know the stock's standard deviation.
Given the following information, calculate the risk-adjusted return. 91-day T-bill rate: 4% Actual return: 14% Beta = 1.4 CPI: 3% Standard deviation: 5.0
Any question asking about the risk-adjusted return is going to be referring to the Sharpe ratio. This is shown as a simple number and is calculated by subtracting the risk-free rate (91-day T-bill) from the actual return and dividing that remainder by the standard deviation. In this example, 14% − 4% = 10% divided by 5 = 2. So actual return minus (91 day tbill or the risk free rate) divided by SD equals the risk adjusted retuen or the sharpe ratio
The total return of a mutual fund is equal to
As with all securities, total return includes unrealized gains or losses. In the case of mutual funds, the total return also assumes reinvestment of all dividend and capital gains distributions.
The current yield on a stock is computed by dividing the annual dividend rate by the current market price. With EPS of $2.50 and a 40% payout ratio, the annual dividend is $1.00. This dollar divided by the current market price of $50.00 results in a current return of 2%.
During the past year, the market price of Kapco common stock has increased from $47 to $50 per share. Over that period, Kapco's earnings per share (EPS) have increased from $2.00 to $2.50 per share, and their dividend payout ratio has decreased from 50% to 40%. Based on this information, the current yield on Kapco common stock is
In the formula for determining the real rate of return,
In computing the real rate of return, which represents inflation-adjusted compounding (or discounting), a formula is applied in which the rate of inflation (usually as measured by the CPI) is subtracted from the investor's rate of return.
An investment is made of $10,000. At the end of the year, $500 in nonqualifying dividends has been received and the value of the investment is $10,500. If the investor is in the 30% tax bracket, the after-tax yield is
The only return (as far as yield is concerned) is the $500 of dividends. Remember, nonqualifying dividends do not "qualify" for the 15% rate. Subtracting 30% for taxes leaves $350 which, when divided by the $10,000 initial cost, is an after-tax yield of 3.5%. If the question had asked about total return, then the $500 unrealized profit would have been included, although there would have been no tax on it.
An investor purchases $10,000 of A-rated debentures in early January. At the end of the year, $500 in interest has been received and the value of the investment is $9,500. If the investor is in the 25% tax bracket, the after-tax yield is
The only return (as far as yield is concerned) is the $500 of interest. Subtracting 25% for taxes leaves $375 which, when divided by the $10,000 initial cost, is an after-tax yield of 3.75%. If the question had asked about total return, then the $500 unrealized loss would have been included, although there would have been no tax benefit to it because it is only a "paper" loss.
Risk-adjusted return is calculated by
The return from a security can be adjusted for the risk associated with it by subtracting the risk-free rate from the security's actual return and then dividing that by its standard deviation, the basic measure of unsystematic risk. This is commonly known as the Sharpe ratio.
A client purchased a security for $60 and sold it 1 year later for $59. If he received 4 quarterly dividends of $0.50 each during the period, his total percentage return would be
The total return on an investment is the sum of the capital gains/losses plus any income distribution such as dividends or interest. In this case, the client had a capital loss of $1 ($60 − $59 = $1), which was offset by $2 (4 × $0.50 = $2) in dividend distributions for a total dollar return of $1. In percentage terms, the return is calculated by dividing the dollar return amount by the total invested or $1 divided by $60 = 1.67%.
f in today's terms, the annual retirement income needed by the client is $15,000. What would be the approximate amount required after three years, given an inflation rate of 4%?
This is simply a compound interest calculation: $15,000 × 1.043= $16,872. Enter $15,000 into the calculator and multiply by 104% three times in a row. Of course, there is always a short-cut. The needs increase by 4% each year. Without compounding, that is $600 per year ($15,000 x 4% = $600). Three years at $600 per year is a total of $1,800 additional needed. That brings the client's needs to $16,800. That doesn't include the compounding so the answer will be slightly higher (and that always works on the exam).
What is the total return on a 1-year, newly issued (365 days to maturity) zero-coupon bond priced at 950?
To determine the total return on this zero-coupon bond, the $50 capital appreciation is divided by the cost of the bond (in this case, $50 divided by $950 equals a total return of 5.26%). Total return of a zero-coupon bond is made up entirely of the difference between the cost of the bond and the sale or maturity price of the bond.
A portfolio manager's performance is often measured against a benchmark such as the S&P 500. A manager whose performance beats the benchmark by taking greater risk than the S&P 500 may not have had superior returns as measured on
a risk-adjusted basis
Risk-adjusted return is calculated by
dividing the security's return in excess of the risk-free rate by its standard deviation This is the Sharpe ratio.
The calculation of yield to maturity assumes reinvestment of the bond's interest at the coupon rate. Therefore, if the investor was only able to do less than that, the holding period return would be decreased. This is part of the concept of internal rate of return (IRR), which takes into consideration the time value of money (compounding). It is tempting to choose the answer "a call at a discount," but bonds are never called at a price below par. Just keep it simple: If the question says you can earn less than the YTM, your return will be lower than the quoted YTM.
the coupons were reinvested at a rate below the yield to maturity
In general, the favored way of measuring the performance of a money manager is by
the most common one is to compare it to that of a benchmark portfolio or index that parallels the manager's style.
