How do you calculate the weight of a risk free asset in a combination portfolio?

CFA Level II
#1

[original post removed]

#2

there are similar questions like this in Qbank:

set up an equation like this:

expected port return = x * (expected return of risky) + (1-x) (risk free) with x being the weight of risky asset

solve for x and you should get it

#3

It could also be based on the expected volatility of the combined portfolio? Thanks…

#4

I’ve devised a formula. The weight to risk free asset in a two asset portfolio can be estimated based on either the required risk of the portfolio (SDp) or required return of the portfolio(Rp).

  • Portfolio risk

Wrf = (SDr-SDp)/SDr

where, Wrf = weight of the risk free asset

SDr = Standard deviation of the risky asset

SDp = required Standard deviation of the portfolio

  • Portfolio return

Wrf= (Rp-Rr)/(Rrf-Rr)

where, Wrf = weight of the risk free asset

Rp = required return for the portfolio.

Rr = return of the risky asset

Rrf = return of the risk free asset

Hope it helps.