This question explores uncertainty in investing. Assume you plan to invest in a broad-based equity index. You start with a zero balance account. Each year, you plan to contribute an extra

$10,000 at year-end. (Assume annual compounding and uncorrelated market returns from year to year.) (Use @Risk tool in excel)

a) If you invest (and contribute) for 30 years and the equity index return each year is normally distributed with expected return of 10% and standard deviation 20% (i.e., a different realized return each year), what is the expected value of your investment account in 30 years (just after your lastpayment)?

b) What is the likelihood that you end up with less than $600,000 in 30 years (i.e.,twice what youcontributed)?

Parts A & B
	Beginning Balance	$0.00
	Contribution	$10,000.00
	Expected Return	10%
	Standard Deviation	20%
	Expected Value of Investment
	Expected Value of Investment (pasted as value)
	Likelihood of less than $600,000
	Likelihood of less than $600,000 (pasted as value)

c) How does the expected balance and likelihood change if you move your money to cashin years where the realized index return in the previous year was negative? (Note: You still make a contribution to your account every year, but your allocation to the market is zero in years where the prior year realized market return was negative. At any given point in time, your entire portfolio is either 100% in the market or 100% incash.)

Beginning Balance	$0.00
Contribution	$10,000.00
Expected Return	10%
Standard Deviation	20%
Expected Value of Investment
Expected Value of Investment (pasted as value)
Likelihood of less than $600,000
Likelihood of less than $600,000 (pasted as value)

d) Let's explore the assumption of uncorrelated market returns. The accompanying spreadsheet provides annual realized market excess returns. Run the followingregression of current year returns on last-year returns (you'll need to lag the returns one year to form thex-variable):

= + +

1

Estimate of coefficient rho:
t-statistic of coefficient rho:
Estimate of intercept:
t-statistic of intercept:
Interpretation
Year	Mkt-RF
1927	0.2960
1928	0.3545
1929	-0.1925
1930	-0.3117
1931	-0.4527
1932	-0.0973
1933	0.5672
1934	0.0322
1935	0.4476
1936	0.3206
1937	-0.3492
1938	0.2833
1939	0.0286
1940	-0.0712
1941	-0.1038
1942	0.1615
1943	0.2806
1944	0.2093
1945	0.3833
1946	-0.0671
1947	0.0296
1948	0.0107
1949	0.1911
1950	0.2883
1951	0.1921
1952	0.1180
1953	-0.0105
1954	0.4934
1955	0.2375
1956	0.0591
1957	-0.1316
1958	0.4346
1959	0.0976
1960	-0.0146
1961	0.2481
1962	-0.1290
1963	0.1784
1964	0.1254
1965	0.1052
1966	-0.1351
1967	0.2449
1968	0.0879
1969	-0.1754
1970	-0.0649
1971	0.1178
1972	0.1305
1973	-0.2624
1974	-0.3574
1975	0.3245
1976	0.2189
1977	-0.0827
1978	0.0103
1979	0.1308
1980	0.2212
1981	-0.1813
1982	0.1066
1983	0.1375
1984	-0.0606
1985	0.2491
1986	0.1012
1987	-0.0387
1988	0.1155
1989	0.2049
1990	-0.1395
1991	0.2917
1992	0.0623
1993	0.0821
1994	-0.0411
1995	0.3121
1996	0.1597
1997	0.2597
1998	0.1946
1999	0.2056
2000	-0.1760
2001	-0.1520
2002	-0.2276
2003	0.3075
2004	0.1072
2005	0.0309
2006	0.1060
2007	0.0104
2008	-0.3835
2009	0.2827
2010	0.1739
2011	0.0047
2012	0.1629
2013	0.3521

What is the estimate and t-statistic for the coefficient ? What is the estimate and t- statistic for the intercept ? Please interpret both economically and statistically.