What is the Expected Value?

Expected Value is a very critical term in Finance. We want to know the ‘Expected Value’ of some variables to estimate some things.

Let's look at different perspectives of Expected Value.

Firstly I have to explain that I try to use real examples when I talk about Expected Value. Because I think it will be more understandable than non-real examples.

In the below table we see my BIST portfolio with weights at the end of July.

I have 13 stocks and most of my money in BIMAS.

When I want to invest my money in a public company, I want to know some critical information about that company. First of all I want to know that is that company is suitable for investment. I use some critical methods to learn this critical information. After this critical investigation, I estimated the price for that company. If I have an acceptable speard between my estimate and stock price, I invest my money.

Let's look at the table below.

In this table we see some ‘Expected Values’. These ‘Expected Values’ are mean value of my expectations and others expectations like BofA or GarantiBBVA Yatirim. 

When I divide ‘Expected Price' to ‘Current Price’ and subtract 1, I find ‘Expected Return’. For example this value is 19,69% for BIMAS.

Remember, I have had some weights like BIMAS’ 29,82%.

If I multiply ‘Expected Return’ and ‘Stock Weight in Portfolio’, I find ‘Weighted Expected Return’ for each stock.

When I sum all of these ‘Weighted Expected Return’ I find ‘Expected Return of Portfolio’.

ERp=w1ER1+w2ER2+w3ER3+w4ER4…. +wnERn

So this means that, If our estimates about ‘prices’ occur, we can gain 39,13% of all of our portfolio.

This was the first definition of the expected value and, noticeably, contains no historical data.

We can also give another definition of expected value.

Assume that you don’t have forward estimates for our stocks. But you want to have ‘Expected Return’ of your portfolio and after that maybe you may want to calculate your portfolio’s standard deviations. If you don’t have enough information about the future you try to use historical data for your estimates.

You use some data. For example I have collected historical prices for my own stocks. When I have taken mean of historical returns for each stock, I have known that I can use it these information for ‘Expected Value’. 

So these are ‘Expected Returns’ but these ‘Returns’ are different from our ‘Future Expected Return’. We can use these for when we want to calculate our portfolio risk.