Question

“Capital allocation line (CAL) must always be a straight line” – Is this statement true? Explain with examples

Answer 1

The Capital allocation line (CAL) has an intercept equal to the risk-free rate. It is a straight line through the point representing the risk-free asset and the risky portfolio. So CAL is a straight line.

Firstly, we need to know, what is Capital allocation line- So here it goes.

Capital allocation line (CAL) is a graph to measure the risk of risky portfolio and risk-free assets for an investor. This helps investors to decide how much to invest in the risky asset and the risk free asset.

No lets talk about the slope of Capital allocation line (CAL)-

The slope of the CAL = (the expected return of the market - the risk-free rate) / (the standard deviation of returns on the market portfolio)

Here slope measures the trade-off between risk and return, It means the steeper the CAL, the higher the expected returns received by the investor for taking risk.

It will also be good to prefer a steeper CAL rather than a flatter one.

Capital allocation line (CAL) is sometimes also known as Capital Market Line (CML). It is when the point of tangency is the market portfolio, the capital allocation line is the capital market line. The CML is a straight line, that means that all the portfolios on the CML are perfectly positively correlated.The equation of the CML is:

E(RP) = RF + [(E(RM) – RF)/SDM] SDp

where:
E(RM) = the expected return on the market portfolio
SDM = the standard deviation of the market portfolio
RF = the risk-free rate, and expected risk premium on the tangency portfolio=[E(RT) – RF]

where, Intercept = risk-free rate, RF.

Slope= [(E(RT) – RF) /SDT] =as the slope of the capital allocation line is equal to the expected risk premium on the tangency portfolio divided by the standard deviation of the tangency portfolio.