# 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(r . Investment f is a risk-free asset (typically
T-bills are considered risk-free) and has a return, r .
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.

_{p}), and a given level of risk_{f}, and zero risk,
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(r

_{c}), or the expected return for portfolio C, is a weighted average of the rates of return on P and f (i.e. E(r_{c})= w*E(r_{p}) + (1-w)*r_{f}). Since asset f is riskless, the riskiness of C is completely dependent on w, the weight in the risky asset, and s_{p}, the riskiness of risky asset P (i.e. s_{c}= w*s_{p}). 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.