This applet looks at combining two investments, P and f,in a portfolio that we will call the complete portfolio, C. [br]We assume the investment P is a portfolio of all risky assets and has an expected return on[br]investment, E(r[sub]p[/sub]), and a given level of risk [math]\sigma_p=0[/math].  Investment f is a risk-free asset (typically[br]T-bills are considered risk-free) and has a return, r[sub]f[/sub], and zero risk, [math]\sigma_f=0[/math]. [br]Given the expected returns, levels of risk, and weights of investment in the[br]two assets, P and f, one can compute the expected return and level of risk for[br]the complete portfolio, C. Changing the weight of investment in the risky[br]asset, w, moves C along the risk/return curve. Changing the levels of expected[br]return and risk features of P and f moves the risk-return curve itself.

[br]The basic assumption is that portfolio C is achieved by[br]investing w in risky asset P and (1-w) in risk-free asset f. Then E(r[sub]c[/sub]), or the expected return for[br]portfolio C, is a weighted average of the rates of return on P and f [br](i.e. E(r[sub]c[/sub])= w*E(r[sub]p[/sub]) + (1-w)*r[sub]f[/sub]). Since asset f is riskless, the riskiness of C is completely dependent on w, [br]the weight in the risky asset, and s[sub]p[/sub], the riskiness of risky asset P [br](i.e. s[sub]c[/sub] = w*s[sub]p[/sub]).  Notice that changing w moves the complete portfolio, C,[br]along the risk-return curve, while changing the other parameters moves the[br]curve itself. When one investment is risk free, then the risk-return curve is a[br]simple linear function.