1	A risk-averse investor is considering two possible assets to be held on a standalone basis. The possible returns and related probabilities (i.e. the probability distributions) for each assets are as follows:
	Asset X		Asset Y
	Prob	rx	ry			Review Thought: Why do we care about a lower SD or CV - given returns are the same? Would the answer change if the investor had a higher appetite for Risk?
	5%	-10%	-4%
	20%	2%	1%
	50%	7%	6%
	20%	8%	10%
	5%	12%	12%
	100%
	Considering both its return and relative risk, which asset is preferred? Why?
	Answer:
	Which asset?
	Why?
						Or, alternatively -
						Asset X						Asset Y
		Asset X	Asset Y			1	2	3	3			1	2	3	3
	Prob	rx	ry			Return x Prob	Deviation from Mean	Deviation Squared	Deviation Squared x Probability			Return x Prob	Deviation from Mean	Deviation Squared	Deviation Squared x Probability
	5%					0.00%	0.00%	0.00%	0.00%			0.00%	0.00%	0.00%	0.00%
	20%					0.00%	0.00%	0.00%	0.00%			0.00%	0.00%	0.00%	0.00%
	50%					0.00%	0.00%	0.00%	0.00%			0.00%	0.00%	0.00%	0.00%
	20%					0.00%	0.00%	0.00%	0.00%			0.00%	0.00%	0.00%	0.00%
	5%					0.00%	0.00%	0.00%	0.00%			0.00%	0.00%	0.00%	0.00%
	Mean	0.00%	0.00%		Mean	0.00%		Variance	0.00%		Mean	0.00%		Variance	0.00%
	St Dev	0.00%	0.00%					Standard Deviation	0.00%					Standard Deviation	0.00%
	CV	#DIV/0!	#DIV/0!					CV	#DIV/0!					CV	#DIV/0!
		?: If CV > 100%
	Guesstimated Mean for X and Y? Could be 2% or 7%? Why not?
2	You are a risk-averse investor. Suppose two stocks had the following historical returns:
		Stock A	Stock B	Portfolio
	Year 1	4%	-3%	0.5%
	Year 2	-4%	3%	-0.5%
	Year 3	10%	10%	10.0%
	Year 4	15%	9%	12.0%
	Year 5	6%	12%	9.0%
	Further suppose you have 3 investment options - a) hold only Stock A, b) hold only Stock B or c) hold a portfolio consisting of 50% of each stock. From a risk perspective only, which would you choose? Why?
	Ans.
		Stock A, stock B or the Portfolio?
		Why?
		Stock A	Stock B	Portfolio
	Year 1	4%	-3%	0.5%
	Year 2	-4%	3%	-0.5%
	Year 3	10%	10%	10.0%
	Year 4	15%	9%	12.0%
	Year 5	6%	12%	9.0%
	Mean
	St. Dev
	CV	#DIV/0!	#DIV/0!	#DIV/0!
			Correlation between A & B
3	Given the information below, what is the value of beta for this stock?
	There will be two-step process needed to solve this.
	1) Solve for the rate of return to the stock using the constant dividend growth model.
	2) Plug that answer into the Security Market Line (SML) formula to solve for beta.
	P0 =	$70	Use this with the constant dividend growth model.
	D1 =	$1.50	Use this with the constant dividend growth model.
	g =	3.0%	Use this with the constant dividend growth model.
	rrf =	2%	Use this with the SML formual.
	rm =	10%	Use this with the SML formual. Note that this is the market return.
	Answers
	a.	0.35
	b.	0.39
	c.	0.45
						Review Thought: In step 2, any questions on rearranging the equation to isolate, and then solve for, Beta?
	Answer:
	Step 1	Find rs:
		r s= D1/P0 + g
	Step 2	Use the CAPM to find beta:
		rs = rRF + (rM - rRF)b
		Please contact me with questions on solving for 'beta'.
4	Suppose you have the following information about a stock:
	Expected Return
	D0 =	$3.00
	P0 =	$45
	g =	2.0%
	Required Return
	rrf =	2%
	rm =	10%	Note that this is the market return.
	b =	0.9
	Calculate the expected return on a stock, use the Constant Dividend Growth model in your analysis.
	Next, calculate the required return on a stock using the Security Market Line (SML) formula.
	With that background in mind, address the following questions.
	a) Is this stock in equilibrium? Explain your reasoning.
	b) If it is not in equilibrium, determine the equilibrium price.
	Answer:
	a. Yes or No
	Explain
	b. Equilibrium Price
	Expected return
	rs =	D0 x (1+g)/P0 + g
	rs =
	Required Return
	rs =	rrf + b (rm - rrf)
	rs =
	b. Expected return < Required return. Sell stock reducing its price until the Expected return = Required return.
	Plug the required return as calculated in the CAPM into the Constant Dividend Growth model.
	P0 =	D0 x (1+g)/(rs - g)
	P0 =
5	You are given the following information on the S&P 500 and the stock price of ABC Corporation.
	Calculate the following metrics:
	a.	Average annual return for each.
	b.	Average annual standard deviation for each.
	c.	Minimum monthly return.
	d.	Maximum monthly return.
	e.	Correlation between the market and ABC corporation.
	f.	Beta calculated using the correlation coefficient & standard deviation formula.
	Month	Market Level (S&P 500 Index) at Month End	Market's Return	ABC Stock Price at Month End	ABC's Return
	March 2022	1,408.47	3.1%	$56.51	-2.2%
	February 2022	1,365.68	4.1%	$57.76	0.1%
	January 2022	1,312.41	4.4%	$57.68	18.4%
	December 2021	1,257.60	0.9%	$49.80	-8.3%
	November 2021	1,246.96	-0.5%	$54.30	0.6%
	October 2021	1,253.30	12.8%	$53.99	2.8%
	September 2021	1,131.42	-7.2%	$52.53	-2.7%
	August 2021	1,218.89	-5.7%	$53.99	11.3%
	July 2021	1,292.28	-2.1%	$48.51	-8.8%
	June 2021	1,320.64	-1.8%	$53.17	-1.8%
	May 2021	1,345.20	-1.4%	$54.16	-7.3%
	April 2021	1,363.61	2.8%	$58.42	9.4%
	March 2021	1,325.83	-0.1%	$53.39	10.4%
	February 2021	1,327.22	3.2%	$48.38	-1.5%
	January 2021	1,286.12	2.3%	$49.10	10.7%
	December 2020	1,257.64	6.5%	$44.34	13.0%
	November 2020	1,180.55	-0.2%	$39.23	-12.8%
	October 2020	1,183.26	3.7%	$44.97	12.5%
	September 2020	1,141.20	8.8%	$39.96	-4.7%
	August 2020	1,049.33	-4.7%	$41.93	11.0%
	July 2020	1,101.60	6.9%	$37.78	-4.4%
	June 2020	1,030.71	-5.4%	$39.51	17.0%
	May 2020	1,089.41	-8.2%	$33.78	-21.3%
	April 2020	1,186.69	1.5%	$42.92	11.1%
	March 2020	1,169.43	5.9%	$38.62	-8.6%
	February 2020	1,104.49	2.9%	$42.25	5.3%
	January 2020	1,073.87	-3.7%	$40.14	4.9%
	December 2019	1,115.10	1.8%	$38.26	15.4%
	November 2019	1,095.63	5.7%	$33.16	-8.2%
	October 2019	1,036.19	-2.0%	$36.11	12.7%
	September 2019	1,057.08	3.6%	$32.04	-1.1%
	August 2019	1,020.62	3.4%	$32.41	13.0%
	July 2019	987.48	7.4%	$28.69	-16.9%
	June 2019	919.32	0.0%	$34.51	9.5%
	May 2019	919.14	5.3%	$31.52	4.3%
	April 2019	872.81	9.4%	$30.23	27.6%
	March 2019	797.87	8.5%	$24.16	3.3%
	February 2019	735.09	-11.0%	$23.38	-17.1%
	January 2019	825.88	-8.6%	$28.20	-3.6%
	December 2018	903.25	0.8%	$29.24	18.1%
	November 2018	896.24	-7.5%	$24.76	-15.2%
	October 2018	968.75	-18.9%	$29.21	-4.0%
	September 2018	1,166.36	-9.1%	$30.43	-27.4%
	August 2018	1,282.83	1.2%	$36.83	17.3%
	July 2018	1,267.38	-1.0%	$31.41	-8.1%
	June 2018	1,280.00	-8.6%	$34.18	-8.6%
	May 2018	1,400.38	1.1%	$37.38	-10.9%
	April 2018	1,385.59	4.8%	$41.95	10.2%
	March 2018	1,322.70	NA	$38.07	NA
	Answers:
	Description of Data		Market		ABC
	a. Average return (annual):
	b. Standard deviation (annual):
	c. Minimum monthly return:
	d. Maximum monthly return:
	e. Correlation between ABC and the market:
	f. Beta: babc = pabc,M (abc / M)