You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 18% and a standard deviation of 21% and a Treasury bill with a rate of return of 4%. How much money should be invested in the risky asset to form a portfolio with an expected return of 13%?

The amount of money invested in risky asset = $6428.57

Explanation:

The portfolio return is made up of the returns of the individual returns of securities in a portfolio multiplied by their weight in the portfolio.

Thus the formula for portfolio retyurn is,

Portfolio return = wA * rA + wB * rB + + wX * rX and so on

Where,

Plugging in the values in the formula,

let x be the weight of investment in risky asset

then x-1 is weight of investment in risk free asset

0.13 = x * 0.18 + (1-x) *0.04

0.13 = 0.18x + 0.04 - 0.04x

0.13 - 0.04 = 0.14x

0.09 / 0.14 = x

x = 9/14 or 0.6429 or 64.29%

The amount of money invested in risky asset is 9/14 * 10000 = $6428.57

ans.

heterothermic organisms include those organisms that can switch between homeothermic (having body temperature higher than environment) and poikilothermic (having variation in internal body temperature) strategies.

some migratory birds show heterothermy as they decrease their metabolic rate during cold nights to keep their body temperature low. drop in metabolic rate allows increase in production efficiency of birds that reduces the internal body temperature to make it equal to external cold temperature during cold nights.

thus, the correct answer is 'birds allow their temperature drop in order to increase their production efficiency.'

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