1. Jacob (from Twilight) can obtain an 85 percent loan with an 8 percent interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 95 percent loan at an 8.5 percent rate with the same loan term. The borrower plans to own the property for the entire loan term.
a. What is the incremental cost of borrowing the additional funds? (Hint: the dollar amount of the loan doesn't affect the answer.)
b. How would your answer change if two points were charged on the 95 percent loan?
c. Would your answer to part (b) change if the borrower planned to own the property for only five years
|
|
Stock
|
House
|
REIT
|
Bond
|
|
Year 1
|
30%
|
35%
|
11%
|
4%
|
|
Year 2
|
13%
|
40%
|
12%
|
5%
|
|
Year 3
|
14%
|
17%
|
31%
|
6%
|
|
Year 4
|
-5%
|
-25%
|
32%
|
-1%
|
|
Year 5
|
-2%
|
-11%
|
12%
|
-2%
|
|
Year 6
|
8%
|
9%
|
-10%
|
3%
|
|
Year 7
|
-8%
|
-22%
|
4%
|
-1%
|
|
Year 8
|
-13%
|
-31%
|
1%
|
-2%
|
|
Year 9
|
18%
|
40%
|
-2%
|
-3%
|
|
Year 10
|
23%
|
50%
|
-5%
|
-4%
|
A. Given the information above, calculate the mean, the standard deviation for each asset.
B. Calculate the correlation between Stock Reit, Stock House and Stock Bond.
Comment on your results.
C. Calculate the correlation between House Reit, and House Bond.
Comment on your results.
D. Let us assume that you can allocate 25% on each asset. Calculate the Rp or rate of return on the portfolio.
E. Let us assume that you can allocate 25% on each asset. Calculate the standard deviation of the portfolio.
F. Calculate the Sharpe Ratio of each asset given a T-bill rate of 1.7% and comment on your results.
G. Calculate the Sharpe Ratio the entire portfolio given a T-bill rate of 1.7% and comment on your results.
2. The following table gives the NPI total return for a three year(12-quarter) period for Boston and San Francisco.
|
YYQ
|
Boston
|
San Francisco
|
|
2003.1
|
0.0024
|
0.0141
|
|
2003.2
|
0.0098
|
0.0050
|
|
2003.3
|
-0.0082
|
0.0078
|
|
2003.4
|
0.0156
|
0.0296
|
|
2002.1
|
0.0325
|
0.0429
|
|
2002.2
|
0.0181
|
0.0248
|
|
2002.3
|
0.0427
|
0.0421
|
|
2002.4
|
0.0655
|
0.0309
|
|
2001.1
|
0.0301
|
0.0439
|
|
2001.2
|
0.0301
|
0.0393
|
|
2001.3
|
0.0520
|
0.0433
|
|
2001.4
|
0.0487
|
0.0447
|
Compute the following quarterly statistics for both cities to the nearest basis point, and answer the subsequent questions.
a. The arithmetic average return and the geometric return.
b. The standard deviation of the return.
c. Now compute the quarterly Sharpe ratio for each. The Sharpe ratio is a measure of risk-adjusted return performance, defined as the risk premium divided by the volatility. Assume that the average quarterly return to Treasury Bonds during the period in question was 1.70%. Which city had the better Sharpe ratio.
2. Historical data for the LOL and SOCUTE are as follows:
|
|
LOL Common Stock Fund
|
SOCUTE Real Estate Fund
|
|
Period Ending
|
Unit value
|
Quarterly Dividend
|
Unit Value
|
Quarterly Dividend
|
|
Quarter
|
|
|
|
|
|
1
|
$701.00
|
$8.28
|
$70.00
|
$2.17
|
|
2
|
752.50
|
8.11
|
80.05
|
2.14
|
|
3
|
850.52
|
10.30
|
90.80
|
2.01
|
|
4
|
953.75
|
9.81
|
100.50
|
2.01
|
|
5
|
1047.57
|
12.05
|
99.14
|
1.87
|
|
6
|
1221.70
|
14.17
|
95.50
|
1.81
|
|
7
|
1443.90
|
17.18
|
93.77
|
1.79
|
|
8
|
1263.31
|
14.91
|
80.31
|
1.54
|
|
9
|
1258.56
|
13.84
|
77.34
|
1.49
|
|
10
|
1526.72
|
18.32
|
76.53
|
1.44
|
|
11
|
1616.81
|
19.73
|
78.42
|
1.51
|
|
12
|
1624.08
|
19.98
|
79.01
|
1.53
|
|
13
|
1560.25
|
18.88
|
81.75
|
1.55
|
a) Calculate the quarterly HPR for each investment.
b) Calculate the arithmetic mean HPR, the standard deviation of HPRs, for each fund.
c) Was there any correlation between returns on the LOL fund and SOCUTE?
d) Would a portfolio that contained equal amounts of LOL securities and SOCUTE have provided any investment diversification? Why?