Question

1. Describe what is meant by the Capital Allocation Line and how it is used in portfolio construction. (10 marks)

2. What are the potential drawbacks of using standard deviation to measure the risk of an asset, and what other measures could be employed?(10 marks)

3. Describe what is meant by efficient markets, and what factors may cause markets to deviate from efficiency.(10 marks)

Answer 1

Capital Allocation Line(CAL):

1. Capital Allocation Line is also called Capital Market Line in modern portfolio theory.
2. Line is created by taking all possible combinations of RiskFree and Risky Assets.
3. Line shows relationship between Risk(Standard Deviation on x-axis) and Expected Return(on y-axis)
4. Line hence shows for a given risk level, how much return can be earned by the investor.
5. Slope of this line is called "Reward to Variability" ratio.
6. Slope of the line is positive, which indicates that as "Variability" or risk increases, "Reward" or expected return also increases.
7. Every point on the CAL has 2 values -
   1. Expected Return(on y-axis) = weight of risk free asset * Return on risk free asset + weight of risky asset * Return on risky asset
   2. Standard Deviation(on x-axis) = weight of risk free asset * standard deviation of risky asset [Remember standard deviation of risk free asset is zero]

How CAL is used in Portfolio Construction:

1. First Portfolio Frontier or Efficient Frontier is calculated.
2. This contains all possible combinations of assets with different weights assigned to them, which are mapped on to a graph showing risk(standard deviation) on the axis and corresponding return on the y axis.
3. Finally investor combines the risk free asset with the risky asset on the efficient frontier.
4. Optimal Portfolio is the point where CAL is tangent to the Efficient Frontier.
5. This is the optimal portfolio because slope of tangent line to efficient frontier is highest. Any other line passing through point (0,Rf) which denotes risk free asset and Efficient Frontier will have a lesser slope and hence a lesser Reward to Variance Ratio.
   

A Efficient frontier for a 2 asset portfolio is given below -

Remember 2 asset Expected Return and Standard Deviation Formula -

Expected Return = w1*E(R1) + w2*E(R2)
Standard Deviation = (w1^2*SD(1)^2 + w2^2*SD(2)^2 + w1*w2*Rho*SD(1)*SD(2))^1/2

where E(Ri) = Expected return of asset i
Wi = weight of ith asset in portfolio
SD(i) = Standard Deviation of Asset i
Rho = Coefficient of correlation of 2 assets.

A ABC 1 E(R1) 0.15 2 E(R2) 0.05 3 SD(1) 0.12 4 SD(2) 0.08 5 Rho 0.12 w1 0.1 =B9+$B$9 =B10+$B$9 =B11+$B$9 =B12+$B$9 =B13+$B$9 =B14+$B$9 =B15+$B$9 =B16+$B$9 w2 =1-B9 =1-B10 =1-B11 =1-B12 =1-B13 =1-B14 =1-B15 =1-B16 =1-B17 Portfolio SD =POWER(B9^2* $B$3^2+C9^2*$B$4^2+B9*C9*$B$5*$B$3*$B$4,0.5) =POWER(B10^2*$B$3^2+C10^2*$B$4^2+B10*C10*$B$5*$B$3*$B$4,0.5) =POWER(B11^2*$B$3^2+C11^2*$B$4^2+B11*c11*$B$5*$B$3*$B$4,0.5) =POWER(B12^2*$B$3^2+C12^2*$B$4^2+B12*C12*$B$5*$B$3*$B$4,0.5) =POWER(B13^2* $B$3^2+C13^2*$B$4^2+B13*C13*$B$5*$B$3*$B$4,0.5) =POWER(B1412*$B$3^2+C1412*$B$4^2+B14*C14*$B$5*$B$3*$B$4,0.5) =POWER(B15^2*$B$3^2+C15^2*$B$4^2+B15*C15*$B$5*$B$3*$B$4,0.5) =POWER(B16^2*$B$3^2+C16^2*$B$4^2+B16*C16*$B$5*$B$3*$B$4,0.5) EPOWER(B17^2*$B$3^2+C1742*$B$4^2+B17*C17*$B$5*$B$3*$B$4,0.5) Portfolio Return =B9*$B$1+C9*$B$2 =B10*$B$1+C10*$B$2 =B11*$B$1+C11*$B$2 =B12*$B$1+C12*$B$2 =B13*$B$1+C13*$B$2 =B14*$B$1+C14*$B$2 =B15*$B$1+C15*$B$2 =B16*$B$1+C16*$B$2 =B17*$B$1+C17*$B$2

G H J K L M ДА В с 1 E(R1) 15% 2 E(R2) 5% 3 SD(1) 12% 4 SD(2) 8% 5 Rho 12% Portfolio Return wi w2 Portfolio SD 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 Portfolio Return 0.073699932 0.06 0.069687302 0.07 0.068366073 0.08 0.069889055 0.09 0.074081037 0.1 0.080526269 0.11 0.088735111 0.12 0.098266576 0.108773526 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.13 0.14

CAL is shown in the diagram below in red color. The point where CAL touches the efficient frontier is the optimal portfolio with highest reward to variability ratio.

Portfolio Return 0 0.02 0.04 0.06 0.08 0.1 0.12 -