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## Risk Tolerance

**Define**

**Risk tolerance** in english is **Risk Tolerance**.Risk tolerance is a measure to assess the willingness to accept risk of investors.

In other words, with the same level of risk, an investor can decide to choose or not to choose a portfolio.

### Meaning

– Determining the risk tolerance of each investor is to help investors quantify their investment decisions, instead of emotional decisions.

– Assume that each investor can determine the utility (or satisfaction) of holding a portfolio on the basis of the expected return and risk of this portfolio.

Utility value can be thought of as a means of rating investment portfolios. Portfolios with a more attractive risk-return correlation are those with higher utility values.

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Portfolios with the same level of risk have a higher utility score when the expected return is higher, and vice versa.

### How to determine utility value?

Determine the useful value according to the following formula:

U = E(r) – 0.5 x A x σ2 (1)

**In there:**

**U is the useful value**

**A is the coefficient expressing the investor’s risk tolerance**

**The coefficient 0.5 is a statistical convention that shows the relationship between the expected return E(R) and the standard deviation σ2.**

**Comment**

In Equation (1), for a risk-free portfolio, i.e. zero variance, its utility will be equal to the expected return. This provides us with a favorable standard by which to evaluate investment portfolios.

Different investors will have a different A-factor, depending on the sentiment and the volume of assets that the investor is holding. However, it is difficult to assess an investor’s risk tolerance.

### For example

An investor must choose between portfolios X and Y, where:

Portfolio X has an expected return of 10% and a standard deviation of 20%.

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Portfolio Y invests in Treasury bills with a risk-free rate of return of 5%.

Assuming an investor has a risk tolerance coefficient A = 3, an average risk tolerance, then the utility value of the portfolio is:

U = E(r) – 0.5 x A x σ2= 0.1 x 0.5 x 3 x (0.2)2 = 0.04 = 4% (Reference: Textbook of Investment Analysis securities, National Economics University Publishing House; Risk Tolerance, Investopedia)

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