As part of an investment team at a large Canadian investment company, you are analyzing the returns of two stocks: TD bank and Sobey. You consider five possible scenarios for the stocks returns depending on how good the economy will be over the coming year. TD bank has a 0.9 correlation with the market portfolio. Sobey has a -0.5 correlation with the market portfolio. The market portfolio has a standard deviation of 10%. The risk free rate is equal to 4%.

Economy scenario	Probability	Return on TD bank stock	Return on Sobey stock
Boom	0.3	30%	8%
Above average	0.2	20%	8%
Average	0.2	10%	10%
Below average	0.2	0%	12%
Recession	0.1	-20%	15%

d) Assume you have a portfolio with $5,000 invested in TD bank and $15,000 invested in Sobey. In addition to the money already invested in both stocks in (d), you have more money available to be invested in a risk-free asset. Your objective is to achieve a portfolio beta of 0.2. How much money (in dollars) do you need to invest in a risk-free asset to change the beta of your portfolio to 0.2?