Question

Suppose that Treasury bills offer a return of about 6% and the expected market risk premium is 8.5%. The standard deviation of Treasury-bill returns is zero and the standard deviation of market returns is 20%. Use the formula for portfolio risk to calculate the standard deviation of portfolios with different proportions in Treasury bills and the market. (Note: The covariance of two rates of return must be zero when the standard deviation of one return is zero.) Graph the expected returns and standard deviations.

What is the slope of the line and what does it describe/signify?

What happens if an investment alternative does not plot on the line?

Answer 1

T-bill return = 6%

So, rf = 6%

Standard Deviation = 0

Market risk premium = rm-rf = 8.5%

S0, rm = 14.50%

Standard Deviation = 0.2

used following formula to calculate portfolio return and portfolio risk/Standard deviation

ER = w1*r1 + w2*r2

SD = weight of market*standard deviation of market

Weight of T-bill	Weight of market	ER	SD
0	1	14.50%	0.1450
0.1	0.9	13.65%	0.1305
0.2	0.8	12.80%	0.1160
0.3	0.7	11.95%	0.1015
0.4	0.6	11.10%	0.0870
0.5	0.5	10.25%	0.0725
0.6	0.4	9.40%	0.0580
0.7	0.3	8.55%	0.0435
0.8	0.2	7.70%	0.0290
0.9	0.1	6.85%	0.0145
1	0	6.00%	0.0000

ER Vs SD Return 0.0000 0.02000.0400 0.0600 0.1000 0.12000.1400 0.1600 0.0800 Risk

Slope = 0.586

The Slope of the line measures the trade-off between risk and return. It tells the amount of return comes with a certain level of risk.

If an investment alternative does not plot on line, it is known as minimum variance frontier. Point on the curve with lowest standard deviation is also called global minimum variance portfolio. Curve above the global minimum variance portfolio is efficient frontier. This curve help to build efficient portfolio for an individual based on his/her risk aversion.