138 Berk/DeMarzo ? Corporate Finance, Second Edition
10-10. Download the spreadsheet from MyFinanceLab that contains historical monthly prices and
dividends (paid at the end of the month) for Ford Motor Company stock (Ticker: F) from August 1994 to August 1998. Calculate the realized return over this period, expressing your answer in percent per month.
Ford Motor Co (F)MonthStock PriceDividendReturnAug-9743.0000.05199Jul-9740.8750.4200.08671Jun-9738.0000.01333May-9737.5000.07914Apr-9734.7500.4200.12096Mar-9731.375-0.04563Feb-9732.8750.02335Jan-9732.1250.3850.00806Dec-9632.250-0.01527Nov-9632.7500.04800Oct-9631.2500.3850.01232Sep-9631.250-0.06716Aug-9633.5000.03475Jul-9632.3750.3850.01189Jun-9632.375-0.11301May-9636.5000.01742Apr-9635.8750.3500.05382Mar-9634.3750.10000Feb-9631.2500.05932Jan-9629.5000.3500.03377Dec-9528.8750.02212Nov-9528.250-0.01739Oct-9528.7500.350-0.06506Sep-9531.1250.01220Aug-9530.7500.06034Jul-9529.0000.310-0.01479Jun-9529.7500.01709May-9529.2500.07834Apr-9527.1250.3100.02084Mar-9526.8750.02871Feb-9526.1250.03465Jan-9525.2500.260-0.08484Dec-9427.8750.02765Nov-9427.125-0.08051Oct-9429.5000.2600.07243Sep-9427.750-0.05128Aug-9429.250Total Return (product of 1+R's)Equivalent Monthly return = (Total Return)^(1/36)-1 =
?2011 Pearson Education
1+R1.051991.086711.013331.079141.120960.954371.023351.008060.984731.048001.012320.932841.034751.011890.886991.017421.053821.100001.059321.033771.022120.982610.934941.012201.060340.985211.017091.078341.020841.028711.034650.915161.027650.919491.072430.948721.678931.45%
Berk/DeMarzo ? Corporate Finance, Second Edition 139
10-11. Using the same data as in Problem 10, compute the
a. Average monthly return over this period.
b. Monthly volatility (or standard deviation) over this period.
Ford Motor Co (F)MonthAug-97Jul-97Jun-97May-97Apr-97Mar-97Feb-97Jan-97Dec-96Nov-96Oct-96Sep-96Aug-96Jul-96Jun-96May-96Apr-96Mar-96Feb-96Jan-96Dec-95Nov-95Oct-95Sep-95Aug-95Jul-95Jun-95May-95Apr-95Mar-95Feb-95Jan-95Dec-94Nov-94Oct-94Sep-94Aug-94Stock Price43.00040.87538.00037.50034.75031.37532.87532.12532.25032.75031.25031.25033.50032.37532.37536.50035.87534.37531.25029.50028.87528.25028.75031.12530.75029.00029.75029.25027.12526.87526.12525.25027.87527.12529.50027.75029.250Dividend0.420Return0.051990.086710.013330.079140.12096-0.045630.023350.00806-0.015270.048000.01232-0.067160.034750.01189-0.113010.017420.053820.100000.059320.033770.02212-0.01739-0.065060.012200.06034-0.014790.017090.078340.020840.028710.03465-0.084840.02765-0.080510.07243-0.051280.4200.3850.3850.3850.3500.3500.3500.3100.3100.2600.260Average Monthly ReturnStd Dev of Monthly Returna. Average Return over this period: 1.60% b. Standard Deviation over the Period: 5.46%
1.60%5.46%
?2011 Pearson Education
140 Berk/DeMarzo ? Corporate Finance, Second Edition
10-12. Explain the difference between the average return you calculated in Problem 11(a) and the
realized return you calculated in Problem 10. Are both numbers useful? If so, explain why.
Both numbers are useful. The realized return (in problem 10.5) tells you what you actually made if you hold the stock over this period. The average return (problem 10.6) over the period can be used as an estimate of the monthly expected return. If you use this estimate, then this is what you expect to make on the stock in the next month.
10-13. Compute the 95% confidence interval of the estimate of the average monthly return you
calculated in Problem 11(a).
Month Aug-98 Jul-98 Jun-98 May-98 Apr-98 Mar-98 Feb-98 Jan-98 Dec-97 Nov-97 Oct-97 Sep-97 Aug-97 Jul-97 Jun-97 May-97 Apr-97 Mar-97 Feb-97 Jan-97 Dec-96 Nov-96 Oct-96 Sep-96 Aug-96 Jul-96 Jun-96 May-96 Apr-96 Mar-96 Feb-96 Jan-96 Dec-95 Nov-95 Oct-95 Sep-95 Aug-95 Jul-95 Jun-95 May-95
Stock Price Dividend Return 44.625
-0.21711 57.000 0.420 -0.02678 59.000 0.13735 51.875
0.13233 45.813 23.680 0.07221 64.813 0.14586 56.563
0.10907 51.000 0.420 0.05884 48.563 0.12936 43.000
-0.01574 43.688 0.420 -0.02255 45.125 0.04942 43.000
0.05199 40.875 0.420 0.08671 38.000 0.01333 37.500
0.07914 34.750 0.420 0.12096 31.375 -0.04563 32.875
0.02335 32.125 0.385 0.00806 32.250 -0.01527 32.750
0.04800 31.250 0.385 0.01232 31.250 -0.06716 33.500
0.03475 32.375 0.385 0.01189 32.375 -0.11301 36.500
0.01742 35.875 0.350 0.05382 34.375 0.10000 31.250
0.05932 29.500 0.350 0.03377 28.875 0.02212 28.250
-0.01739 28.750 0.350 -0.06506 31.125 0.01220 30.750
0.06034 29.000 0.310 -0.01479 29.750 0.01709 29.250
0.07834
?2011 Pearson Education
Berk/DeMarzo ? Corporate Finance, Second Edition 141
Month Stock Price Dividend Return Apr-95 27.125 0.310 0.02084 Mar-95 26.875 0.02871 Feb-95 26.125 0.03465 Jan-95 25.250 0.260 -0.08484 Dec-94 27.875 0.02765 Nov-94 27.125 -0.08051 Oct-94 29.500 0.260 0.07243 Sep-94 27.750 -0.05128 Aug-94 29.250 Average Monthly Return Std Dev of Monthly Return Std Error of Estimate = (Std Dev)/sqrt(36) = 95% Confidence Interval of average monthly return
2.35% 7.04%
1.02% 0.31%
4.38%
10-14. How does the relationship between the average return and the historical volatility of individual
stocks differ from the relationship between the average return and the historical volatility of large, well-diversified portfolios?
For large portfolios there is a relationship between returns and volatility—portfolios with higher returns have higher volatilities. For stocks, no clear relation exists.
10-15. Download the spreadsheet from MyFinanceLab containing the data for Figure 10.1.
a. Compute the average return for each of the assets from 1929 to 1940 (The Great Depression). b. Compute the variance and standard deviation for each of the assets from 1929 to 1940. c. Which asset was riskiest during the Great Depression? How does that fit with your intuition? a/b.
Average Variance: Standard deviation: Evaluate:
c. The riskiest assets were the small stocks. Intuition tells us that this asset class would be the riskiest.
10-16. Using the data from Problem 15, repeat your analysis over the 1990s.
a. Which asset was riskiest?
b. Compare the standard deviations of the assets in the 1990s to their standard deviations in
the Great Depression. Which had the greatest difference between the two periods? c. If you only had information about the 1990s, what would you conclude about the relative
risk of investing in small stocks? a. Using Excel:
S&P 500 Small Stocks
Corp Bonds
World Portfolio
Treasury
CPI
S&P 500 2.553% 0.1018 31.904%
Small Stocks 16.550% 0.6115 78.195%
Corp Bonds 5.351% 0.0013 3.589%
World Portfolio 2.940% 0.0697 26.398%
Treasury Bills 0.859% 0.0002 1.310%
CPI
0.0022 4.644%
?2011 Pearson Education
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