The Tolkien Fund has a standard deviation of $20\%,$ and the Lewis Fund has a standard deviation of $34\%.$ You currently have $43\%$ of an investment account invested in Tolkien, and the rest in a risk$-$free asset. This results in your overall account having a standard deviation of X$\%($not given but easy to calculate$).$

You decide to sell your ownership of Tolkien and purchase Lewis, rebalancing your investment account so that now you will own only Lewis and the risk$-$free asset. What portion of your account will need to be invested in Lewis $($with the rest in the risk$-$free asset$)$ so that your overall account will still have the same standard deviation of X$\%$ that it did before?

Express your answer accurate and rounded to $4$ decimal places. If you believed you will need to invest $12\mathrm{.}34\%$ of the account in Lewis, for example, then you would enter $0\mathrm{.}1234.$