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

[jaychou]

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

 

[sooraj]

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

 

[RBA]

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.