Risk Adjusted Return

How to Fairly Estimate Portfolio?

Before we dive into selecting better portfolios, we need to clarify what matters the most for us. Are we prioritizing higher returns, lower risks, or something else?

It's important to note that generally, higher returns come with higher risks.

So, we should evaluate whether expected return is sufficiently high to justify the associated risk.

Therefore, we can use Risk Adjusted Return (RaR) as one of the optimality measures:

Sharpe Ratio

After discussing what is a risk-adjusted return, the next question arises: how can we specifically measure it?

The most common and likely the simplest way to measure risk-adjusted return is through the Sharpe Ratio, which is defined by the following formula:

Here we encounter a new term: risk-free interest rate, which refers to the theoretical return on an investment with no risk of financial loss.

The risk-free rate usually represents the interest rate on government bonds, which are deemed to have minimal risk because they are backed by the government.

When we consider the risk-free rate to be zero, we can interpret it as ratio of the return to the risk. Generally, it reflects ratio of the generated profit to the risk involved.

A portfolio with a Sharpe ratio greater than 1 is generally considered solid.

Here is a code example of computing the Sharpe ratio based on the previously mentioned example, assuming a risk-free rate of 0.01:


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# Defining corresponding returns `R1` and `R2`, corresponding risks `vol1` and `vol2` and risk-free interest rate `r`
R1 = 0.1
R2 = 0.2 
vol1 = 0.02
vol2 = 0.05
r = 0.01

# Computing Sharpe ratios `s1` and `s2`
s1 = (R1 - r) / vol1
s2 = (R2 - r) / vol2

print('Sharpe ratio for the first case:')
print(s1)
print('Sharpe ratio for the second case:')
print(s2)

Here we define variables R1 and R2 for corresponding returns, vol1 and vol2 for corresponding risks and r for interest rate and then computing Sharpe ratios s1 and s2 with a given above formula and standard embedded arithmetic operations.

As we can see, the Sharpe ratio of the first portfolio is higher than that of the second, so we should consider the first portfolio to be more optimal.

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Section 2. Chapter 1