# Portfolios with one risky investments

Author:
Mike May
This applet looks at combining two investments, P and f,in a portfolio that we will call the complete portfolio, C. We assume the investment P is a portfolio of all risky assets and has an expected return on investment, E(rp), and a given level of risk .  Investment f is a risk-free asset (typically T-bills are considered risk-free) and has a return, rf, and zero risk, . Given the expected returns, levels of risk, and weights of investment in the two assets, P and f, one can compute the expected return and level of risk for the complete portfolio, C. Changing the weight of investment in the risky asset, w, moves C along the risk/return curve. Changing the levels of expected return and risk features of P and f moves the risk-return curve itself.
The basic assumption is that portfolio C is achieved by investing w in risky asset P and (1-w) in risk-free asset f. Then E(rc), or the expected return for portfolio C, is a weighted average of the rates of return on P and f (i.e. E(rc)= w*E(rp) + (1-w)*rf). Since asset f is riskless, the riskiness of C is completely dependent on w, the weight in the risky asset, and sp, the riskiness of risky asset P (i.e. sc = w*sp).  Notice that changing w moves the complete portfolio, C, along the risk-return curve, while changing the other parameters moves the curve itself. When one investment is risk free, then the risk-return curve is a simple linear function.