The Tolkien Fund has a standard deviation of 20%, and the Lewis Fund has a standard deviation of 29%. You currently have 57% 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 12.34% of the account in Lewis, for example, then you would enter 0.1234.