Supposing For Example An Individual Has 3 Investment Options: A 50% Chance

Supposing for example an individual has 3 investment options:
a 50% chance of making £1k and equally a 50% chance of losing £1k. This is known as a fair investment. A fair investment is similar to the fair gamble theme, in that it is one in which on average, there is an equal chance of a profit or loss
a 40% chance of making £1k and a 60% chance of losing £1k. This is an unfair investment, whereby on average the individual will make a loss
a 60% chance of making £1k and a 40% chance of losing £1k. This is a favourable investment
Let us now compare the fair investment (equal chance of profit or loss) with another fair investment, which is a 50% chance of either making or losing £2k. Even though both are fair investments, the latter investment is the riskier as the range of possible outcomes is more than the former.
An individual's attitude to risk or risk preference can be classified as risk averse, risk neutral or risk loving.
McLaney (2006) helps to provide definitions of the risk attitudes or states:
a risk averse individual is an individual that is only prepared to take a risk where the expected return is greater than the cost of the project or investment in question, at entry stage
a risk neutral individual is an individual who is prepared to take a risk where the expected return is equal to the cost of the project or investment
a risk loving individual is one who is prepared to take a risk even were the expected return from the investment or project is less than the cost of the investment or project at entry stage, provided that at least one possible outcome has a value greater than the cost of the investment or project at entry stage
An individual's attitude to risk can be determined by analysing whether he will be willing to invest in a fair investment, i.e. one that has an equal chance of making or losing money.
A risk averse individual will not do this and will only invest if the probability of making a profit outweighs the probability of making a loss. This type of individual dislikes risk and will need to be compensated more, in terms of return for the risk he is willing to take. The more risk averse the individual, the more that individual requires, by way of return for him to invest.
A risk neutral investor would not make his investment decision based on the probability of making or losing money. He should focus himself on how much can be made from the investment. Effectively, the risk neutral investor is more concerned about achieving his investment objective in terms of return. When faced with a choice between two investments, the risk neutral investor will choose the one with the higher expected return. If expected returns for both investments are equal, the risk neutral investor could choose either, regardless of the individual asset's risk.
A risk loving investor will make a fair investment.