# Finance stocks question

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If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain for me please.

If
investors’ aversion to risk increased then the risk premium on
high-beta stock increase more than that on a low-beta stock. It is
because the effect of the change in the risk aversion is stronger on
more risky securities than in less riskier securities. Beside this,
there is the positive relationship between risk aversion and the risk
premium. If the risk aversion increases then the risk premium also goes
up causing the slope of the security market line (SML) to become
steeper. The steeper the Security market lines higher the required rate
of return. Risk premium for stock x can be calculated as: Risk premium
of market (RP_{M}) multiply by beta of stock x (β_{x}).

For example,

Market risk premium (RP_{M}) = 6%

Beta for stock X = 0.7

Beta for stock Y = 1.4

Now, calculation of risk premium for stock X and Y.

Risk premium for stock X = Market risk premium X beta

= 6% X 0.7

= 4.2%

Risk premium for stock Y = Market risk premium X beta

= 6% X 1.4

= 8.4%

Again, let’s suppose investors’ risk aversion increase that leads market risk premium to increase from 6% to 8% and beta for those stock remain the same.

Risk premium for stock X = Market risk premium X beta

= 8% X 0.7

= 5.6%

Risk premium for stock Y = Market risk premium X beta

= 8% X 1.4

= 11.2%

The above example clearly shows that risk premium for stock Y which has higher beta increase more than stock X which has lower beta. Therefore, risk premium on a high-beta stock increase more than low beta stock when investors’ aversion to risk increase.

http://dineshperspective.blogspot.com/2011/05/financial-management-problem-and.htmlHope this helps!

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