Relationship of Risk and Return
There is a positive relationship between risk and return because risk and return are interrelated to each other, higher the return and higher the risk. Rational investor are risk averse because they are willing invest in risky assets with compensate by high return by risk premium. Lower levels of uncertainty or risk gives low potential returns, whereas higher level of uncertainty or risk gives high potential returns. The best known to describe risk and return relationship is risk-return trade-off. Risk-return trade-off is a systematic function of investment where money can render higher profits only if the investor is willing to accept the possibility of losses. Risk premium plays a key role of combining risk and return positively.
It is true that investor invest in higher risk with higher return but not always because rational investor is choose among the alternatives that give more return with same level of risk among other securities. On the other hand, securities with lower risk are those chosen by the investors with lower risk appetite. They therefore offer a lower return, and are more indicated for conservative investment strategies. The risk-return trade-off is at the foundation of modern finance, and finding the right balance between return demand and risk exposure is at the basis of good management of a business.
In this example, E(r) is expected return and (σ) is risk whereas A, C & D stock are dominant stocks. Rational investors always invest in such dominant stock because risk-averse investor invests in stock A rather than stock B. The reason to invest in stock A rather than Stock B is that with same level return risk of stock A is less than risk of stock B. Risk taker investor invest in stock D with same level of risk (i.e. 10) by not to invest in stock F.