ASM Manual question 21.8 states:
Half of a portfolio's value is invested in a stock with time-t price S(t), and the other half is invested in a risk-free asset. The portfolio is balanced continuously.
No dividends.
In the solution, they state: If W(t) is the time-t price of the portfolio, the Ito process for W(t) has a return with a 50% weight on alpha and a 50% weight on r.... and the volatility is half of S(t)'s volatility.
How do we know that the volatility of the portfolio is half of S(t)'s volatility?
Half of a portfolio's value is invested in a stock with time-t price S(t), and the other half is invested in a risk-free asset. The portfolio is balanced continuously.
No dividends.
In the solution, they state: If W(t) is the time-t price of the portfolio, the Ito process for W(t) has a return with a 50% weight on alpha and a 50% weight on r.... and the volatility is half of S(t)'s volatility.
How do we know that the volatility of the portfolio is half of S(t)'s volatility?
Proportional Portfolios
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