In: Statistics and Probability

From historical data, the annual rates of return of S&P 500 stocks from 1985 to 2000 are roughly normally distributed. The mean is 9.4%, and the standard deviation is 18.25%. Treating the next 10 years as a simple random sample. What is the probability that the mean annual rate of return is greater than 3% (the current inflation rate)? Round to 3 decimal places

**From historical data, the annual rates of return of
S&P 500 stocks from 1985 to 2000 are roughly normally
distributed.**

**The mean is 9.4% and the standard deviation is
18.25%.**

**Now, we take the next 10 years as a sample.**

**So, the mean return of these 10 years, would follow
normal distribution with mean 9.4 and standard deviation
of**

**We have to find the chance that this mean annual rate of
return is more than 3%.**

**So, if X be the random variable denoting the mean, then
X follows normal with mean 9.4 and standard deviation of
5.7712.**

**So, we have to find**

**Where, phi is the distribution function of the standard
normal variate.**

**From the standard normal table, it becomes**

**So, the required probability, that the mean annual
return would be more than 3%, is 0.867.**

Consider historical data showing that the average annual rate
of return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 20% per year. Assume
these values are representative of investors’ expectations for
future performance and that the current T-bill rate is 5%.
Calculate the expected return and variance of portfolios
invested in T-bills and the S&P 500 index with...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 34% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 5%.
Calculate the utility levels of each portfolio for an investor with
A = 3. Assume the utility...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 29% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 4%.
Calculate the utility levels of each portfolio for an investor with
A = 3. Assume the utility...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 37% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 5%.
Calculate the utility levels of each portfolio for an investor
with A = 2. Assume the utility...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 32% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 4%.
Calculate the utility levels of each portfolio for an investor
with A = 3. Assume the...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 24% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 3%.
Calculate the utility levels of each portfolio for an investor
with A = 2. Assume the utility...

Consider historical data showing that the average annual rate of
return on the S&P 500 portfolio over the past 85 years has
averaged roughly 8% more than the Treasury bill return and that the
S&P 500 standard deviation has been about 27% per year. Assume
these values are representative of investors' expectations for
future performance and that the current T-bill rate is 6%.
Calculate the utility levels of each portfolio for an investor
with A = 2. Assume the utility...

The following data on annual rates of return were
collected from five stocks listed on the New York Stock Exchange
(“the big board”) and five stocks listed on NASDAQ. Assume the
population standard deviations are the same. At the .10
significance level, can we conclude the annual rates of return are
higher on the big board?
NYSE
17.16
17.08
15.51
8.43
25.15
NASDAQ
15.80
16.28
16.21
17.97
7.77
Really important: Use Excel as
described in “How...

Suppose that: S&P 500 index is trading at 2000; index stocks
do not pay any dividends; and you can borrow and lend at 5% per
annum. You have an index portfolio worth $20 million. An index
futures contract with a multiplier of 100 matures in a year – this
means one futures contract represents an index basket of stocks
with a market value of 100 times the index value. How will you
fully hedge your portfolio for a one year...

Historical Realized Rates of Return
Stocks A and B have the following historical returns:
Year
2012
-19.60%
-14.00%
2013
20.00
30.00
2014
12.00
35.30
2015
-1.00
-10.20
2016
31.50
1.80
Calculate the average rate of return for each stock during the
5-year period. Round your answers to two decimal places.
Stock A
%
Stock B
%
Assume that someone held a portfolio consisting of 50% of Stock
A and 50% of Stock B. What would have been the realized rate...

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