adding rf to portfolio decrease or no change sharp/safety fi different, decrease, increase, original, change

amqata

if we add a the Risk free asset to porfolio , does it increase/decrese or no change to the sharp ratio of the portfolio?
the answer is no change, but I don’t agree. say old portfolio return is 5%, add 10 % Rf, 90%*5+10%*rf will be different with original portfloio return, so it will change original sharp and safety first ratio.

cchang

std deviation is reduced as well in proportion.  thus no change.

thecfawannabe

thanks, but….
old portfolio return 5%, but my Rf is 7%, adding Rf, my new portfolio 5%, so are you saying safety first ratio will go up?

rgonzalez

why would you invest in a RISKY PORTFOLIO giving you 5% if your RISK FREE return is 7%?
please get logical in what you post, if you must post.

dontknow1987

shhh cpk123 - there’s only a few days left. I need to pass ;)

RobertA

hey linping think about it this way :
when you combine the risk free asset with the risky portfolio, you are moving along the capital allocation line rather than the original rounded minium variance frontier…the sharpe ratio is the slope of the CAL,so every point on the CAL has the same sharpe ratio. If you move to the right from the Tangency portfolio on the CAL you would be borrowing money to leverage your position in the risky portfolio,if you are splitting money between rf and risky portfolio, you would move to the left of the tangeny portfolio..the rate at which you give up return for less risk,or assume return for more risk is always the same on that CAL.