Question

An investor purchases a share of Synovous Bank stock this morning for $2.80. The investor believes the economy will take one of three conditions in the coming year, and each condition will have an impact on the selling price of the stock. The investor’s beliefs about the economy are shown below:

OUTCOME:	Probability	Synovous Price in One Year
Bad for Banks	0.34	$2.56
Moderate for Banks	0.31	$2.98
Good for Banks	0.35	$3.44

What is the standard deviation for Synovous returns (based on the investor’s returns)?

Answer Format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Answer 1

Bad for Banks:

Investor’s Return = (Price in One Year - Current Price) / Current Price
Investor’s Return = ($2.56 - $2.80) / $2.80
Investor’s Return = -0.0857

Moderate for Banks:

Investor’s Return = (Price in One Year - Current Price) / Current Price
Investor’s Return = ($2.98 - $2.80) / $2.80
Investor’s Return = 0.0643

Good for Banks:

Investor’s Return = (Price in One Year - Current Price) / Current Price
Investor’s Return = ($3.44 - $2.80) / $2.80
Investor’s Return = 0.2286

Expected Return = 0.34 * (-0.0857) + 0.31 * 0.0643 + 0.35 * 0.2286
Expected Return = 0.0708

Variance = 0.34 * (-0.0857 - 0.0708)^2 + 0.31 * (0.0643 - 0.0708)^2 + 0.35 * (0.2286 - 0.0708)^2
Variance = 0.0170558

Standard Deviation = (0.0170558)^(1/2)
Standard Deviation = 0.1306 or 13.06%