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## What does the expected value tell us?

Expected Value (EV) is a forecasted value of an investment. It is calculated by multiplying the possible outcomes by the probability of their occurrence and then adding all those values. EV is the long-run average of random variables. Also, it is the probability-weighted average of all possible values.

An investor can use EV to determine the scenario that will most likely give better return and choose the same. Additionally, investors can calculate the return of an existing investment with the help of EV. Expected Value indicates the average return an investment can make after considering all the possibilities. EV is used by individual investors, companies and organizations to make major investing decisions.

When an investor is unable to determine the state of the market but can guess the likely returns in each state, then the investor can use EV to determine the expected return from the investments.

## How is the expected value used in real life?

Expected value helps in making real life decisions. It allows an individual to compare the best and worst scenarios and expected risk. Expected value gives a probable percentage for each of the outcomes for the decisions taken. In simple terms, EV is the sum of all possible values of a possible outcome for a particular decision.

The expected value is one of the ways way to make an investment decision. It allows us to quantify and incorporate the volatility factor (risk) into the decision making process. In life, everything is a probability. And, expected value rightly incorporates the probability of the best and worst scenario from investments. Hence it is a good measurement to consider while making investment decisions. However, to calculate the values is quite time consuming and a nightmare for non-statisticians.

Theoretically, opting for decisions with a positive EV will eventually result in favourable outcomes. However, EV cannot be the only factor on which one can make investment decisions. It is essential to consider other factors such as risk tolerance levels, age, income, family status, etc.

## What is the expected value of a random variable?

Expected value is an important concept that investors use to estimate the expected returns from their investments. A random variable is used to determine the returns from an investment. A random variable is a set of all possible outcomes from a random experiment. In the case of investments, a random variable is all the possible returns.

The expected value of the random variable is the weighted average of all possible outcomes of the random variable. The weights are the probabilities of each outcome. For a random variable X, the expected value can be calculated as follows:

E(X) = PX1*(X1)+ PX2*(X2)+ ….. + PXn(Xn)

Where,

E(X) is the expected value of the random variable.

PX_{(1to n)} is the probability of each outcome.

X_{(1to n) }is the return from a random variable.

Let’s take an example of an investor Mr Arjun, who invested in financial securities. His portfolio returns are dependent on market conditions. He comes up with the following:

Market Conditions | Probability | Return on Portfolio |

1 | 0.25 | 15% |

2 | 0.25 | -3% |

3 | 0.25 | -5% |

4 | 0.25 | 20% |

The expected return for Mr Arjun will be

E(R) = 0.25*0.15 + 0.25* (-0.03) + 0.25* (-0.05) + 0.25* (0.20)

E(R) = 6.75%

## Does ‘expected’ mean ‘required’?

The expected return is the return an investor expects from an investment. And the required return is the minimum return an investor would accept for it to be worthwhile.

The expected return is the return an investor expects to receive for holding an investment for a tenure. On the other hand, the required return is the minimum return an investor would demand for holding the asset for a tenure instead of holding other assets with similar risk.

The expected return is estimated through statistical methods using a few inputs. At the same time, the required return is the end result that needs to be achieved. One needs to change the inputs to close the gap between the expected and required rate of return.

Expected return helps investors to figure out how much return they can expect on an investment. While the required rate of return helps investors decide if the investment is rewarding.

## What is the difference between NPV and IRR?

#### Net Present Value

Net Present Value (NPV) is the difference between the present value of cash inflows and outflows over a period of time. In other words, it represents the negative and positive cash flows throughout the project’s lifecycle discounted to today. NPV is an intrinsic assessment. The usage of NPV is applicable in finance and accounting, where it is used to assess new ventures, value a business, etc.

#### Internal Rate of Return

Internal Rate of Return (IRR) helps in estimating the profitability of potential investments. The financial metric is a discounting rate that equated the net present value of cash flows to zero.

IRR and NPV give conflicting results when the cashflow timings and patterns are different. Also, in case of mutually exclusive projects where acceptance of one blocks the acceptance of the other, NPV and IRR give contradicting results. NPV might suggest the project manager to accept one project, while IRR may show the other project as more favourable.

Both the financial measurements are used in capital budgeting. NPV and IRR are discounted cash flow methods. Companies use it to determine whether an expansion opportunity or a new investment is worthwhile. In other words, both measures help in deciding if a project is desirable and whether or not it will add value to the company. One uses a percentage representation, while the other as a rupee figure. IRR doesn’t take into consideration the changing factors such as discount rates. In such cases, using the net present value is more suitable for mutually exclusive projects.

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