1. Eli Lilly, Inc shows the following history of dividends and stock price. a.)
ID: 2790429 • Letter: 1
Question
1. Eli Lilly, Inc shows the following history of dividends and stock price.
a.) An investor buys three shares of XYZ at the beginning of 2012, buys another two shares at the beginning of 2013, sells one share at the beginning of 204, and sells all four remaining shares at the beginning of 2014.
b. )What are the arithmetic and geometric average time-weighted rates of return for this investor?
c.) What is the dollar-weighted rate of return? (Hint: Prepare a chart of cash flows for the four dates corresponding to the turns of the year for Jan 1, 2012, to Jan 1, 2015. If your calculator can’t find the IRR, you will have to use a spreadsheet and trial and error.)
2. Assume that you have a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-Bill rate is 7%.
Your client chose to invest 70% of a portfolio in your fund and 30% in a T-Bill money market fund.
a.) What are the expected return and standard deviation of your client’s portfolio?
b.) Suppose your risky portfolio includes the following investments in the given proportions:
Caterpillar, Inc: 27%
John Deere: 33%
Portola Pharmaceuticals: 40%
c.) What is the Sharpe ratio (S) of your risky portfolio and your client’s overall portfolio?
d.) Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL?
3. Refer to the situation in problem two You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected return of 13% with a standard deviation of 25%. Draw the CML and your fund’s CAL on an expected return/standard deviation diagram.
a.) What is the slope of the CML?
b.) Characterize in a paragraph the advantage of your fund over the passive fund.
Explanation / Answer
Question 1:
a.) An investor buys three shares of XYZ at the beginning of 2012, buys another two shares at the beginning of 2013, sells one share at the beginning of 2014, and sells all four remaining shares at the beginning of 2015.
Time
Year
Cash flow form stock buying/selling
Cash flow from Dividend
Total Cash Flow
1/1/2012
0
3* -$100 = -$300
0
-$300.00
1/1/2013
1
2 *-$110 = - $220
3*4 =12
-$208.00
1/1/2014
2
1* $ 90 = $90
5*4 =20
$110.00
1/1/2015
3
4* $95 = $380
4*4 = 16
$396.00
Note: Negative sign for cash outflow and Dividend Paid at Year End therefore assume its cash flow in the next years (at it is very close to Beginning of next Year)
b. )What are the arithmetic and geometric average time-weighted rates of return for this investor?
Yearly Return = {(capital gains + dividend)/price}*100
Return from 2012-2013 = {(110 - 100) + 4} /100 *100 = 14.00%
Return from 2013-2014 = {(90 - 110) + 4} /110 *100 = -14.55%
Return from 2014-2015 = {(95 - 90) + 4} /90 *100 = 10%
Arithmetic mean = (14% -14.55% +10%)/3 = 9.45%/3 = 3.15%
Geometric mean = [(1+14%)*(1-14.55%) *(1+10%)] ^ (1/3) -1
= (1.14 *0.8545 * 1.10) ^1/3 – 1 = 0.0233 = 2.33%
The arithmetic average time-weighted rates of return for the investor is 3.15%
The geometric average time-weighted rates of return for the investor is 2.33%
c.) What is the dollar-weighted rate of return? (Hint: Prepare a chart of cash flows for the four dates corresponding to the turns of the year for Jan 1, 2012, to Jan 1, 2015. If your calculator can’t find the IRR, you will have to use a spreadsheet and trial and error.)
Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2012, to January 1, 2015
Time
Year
Cash flow form stock buying/selling
Cash flow from Dividend
Total Cash Flow
1/1/2012
0
3* -$100 = -$300
0
-$300.00
1/1/2013
1
2 *-$110 = - $220
3*4 =12
-$208.00
1/1/2014
2
1* $ 90 = $90
5*4 =20
$110.00
1/1/2015
3
4* $95 = $380
4*4 = 16
$396.00
IRR
-0.17%
Note: Negative sign for cash outflow
The dollar-weighted return is the internal rate of return (IRR) that can be calculated by discounting from the rate which makes the sum of the present value of each net cash flow to zero.
0 = -$300/ (1+IRR) ^0 - $208/ (1+IRR) ^1 + $110/ (1+IRR) ^2 + $ 396/ (1+IRR) ^3
From trial and error method, we can calculate the value of IRR, which is
IRR = -0.17%
Time
Year
Cash flow form stock buying/selling
Cash flow from Dividend
Total Cash Flow
1/1/2012
0
3* -$100 = -$300
0
-$300.00
1/1/2013
1
2 *-$110 = - $220
3*4 =12
-$208.00
1/1/2014
2
1* $ 90 = $90
5*4 =20
$110.00
1/1/2015
3
4* $95 = $380
4*4 = 16
$396.00
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