Question

The market price of a security is $26. Its expected rate of return is 13%. The risk-free rate is 5%, and the market risk premium is 7.0%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)

Answer 1

The increase in stock risk has lowered its value by 16.09%.

What does market price mean?

• The price at which a good or service can currently be bought or sold is known as the market price.
• The forces of supply and demand determine the market price of a good or service; the price at which the quantity supplied and demanded are equal is the market price.

What is current price and market price?

• Market value is another name for the current price. It is the last traded price for a share of stock or any other security.

According to the question:

• If the security's correlation coefficient with the market portfolio doubles (with all other variables such as variances unchanged), then beta, and therefore the risk premium, will also double. The current risk premium is:  13% - 5% = 8%

The new risk premium would be 16%, and the new discount rate for the security would be: 16% + 5% = 21%

If the stock pays a constant perpetual dividend, then we know from the original data that the dividend (D) must satisfy the equation for the present value of a perpetuity:

Price = Dividend/Discount rate.

26 = D/0.13.

D =26 x 0.13.

D = $3.38.

At the new discount rate of 21%, the stock would be worth:

$3.38/0.21.

= $16.09.

The increase in stock risk has lowered its value by 16.09%.

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