Lecture 1: Risk Aversion and Capital Allocation
Expected return:
To counter the uncertainty in the future returns, we assign particular probabilities to particular
values of return on the basis of the market conditions. The expected return is therefore calculated
as:
𝐸[𝑅] = ∑𝑝(𝑠) ∗ 𝑟(𝑠)
Where p(s) is the probability of return r(s).
To predict the volatility of the expected returns, standard deviation is used which is calculated as:
Portfolio construction:
There are two steps of the portfolio construction-
Selection of the risky assets
Deciding how much to invest in the risky portfolio and how much in the risk free assets. This
is where the expected return and the standard deviation calculations come into play. As they
help us decide the weight of risky assets in the overall portfolio. However the investment
decision ultimately depends on the individual investors, his preferences and his attributes
towards the risk.
Risk Aversion:
A risk averse investor is one who wants greater return for a given level of risk. Therefore a risk
averse investor would never invest in an investment with a risk premium of zero.
Utility:
Although the investors are risk averse, they all have different levels of risk tolerance. This means that
different investors will settle down for different levels of risk and returns. To measure this concept
of risk aversion, we use the utility function. The utility function therefore provides us with an
indifference curve through which an investor can choose between different securities. Higher the
utility value, more attractive is the risk-return profile. Higher returns have higher utility and higher
volatilities have lower utility. There are many functions to calculate the utility value but the one that
we will be using here is:
Here A is the measure of risk aversion. Higher the value of A, more risk averse the investor is. Also in
the equation, higher the value of A, the lower will be the value of utility.
If A=0, the investor is risk neutral.
Expected return:
To counter the uncertainty in the future returns, we assign particular probabilities to particular
values of return on the basis of the market conditions. The expected return is therefore calculated
as:
𝐸[𝑅] = ∑𝑝(𝑠) ∗ 𝑟(𝑠)
Where p(s) is the probability of return r(s).
To predict the volatility of the expected returns, standard deviation is used which is calculated as:
Portfolio construction:
There are two steps of the portfolio construction-
Selection of the risky assets
Deciding how much to invest in the risky portfolio and how much in the risk free assets. This
is where the expected return and the standard deviation calculations come into play. As they
help us decide the weight of risky assets in the overall portfolio. However the investment
decision ultimately depends on the individual investors, his preferences and his attributes
towards the risk.
Risk Aversion:
A risk averse investor is one who wants greater return for a given level of risk. Therefore a risk
averse investor would never invest in an investment with a risk premium of zero.
Utility:
Although the investors are risk averse, they all have different levels of risk tolerance. This means that
different investors will settle down for different levels of risk and returns. To measure this concept
of risk aversion, we use the utility function. The utility function therefore provides us with an
indifference curve through which an investor can choose between different securities. Higher the
utility value, more attractive is the risk-return profile. Higher returns have higher utility and higher
volatilities have lower utility. There are many functions to calculate the utility value but the one that
we will be using here is:
Here A is the measure of risk aversion. Higher the value of A, more risk averse the investor is. Also in
the equation, higher the value of A, the lower will be the value of utility.
If A=0, the investor is risk neutral.
