Drawing a blank. Does adding the RF asset to the tangency portfolio increase your risk adjusted return? What’s the main benefit of adding the risk free asset to the tangency portfolio?
Yes. When you can borrow at the risk free rate you choose the portfolio with the highest Sharpe ratio, as opposed to just the two adjacent corner portfolios.
Agree with NG. Short RF asset and take a long position in excess of 100% of the portfolio with the highest sharpe ratio. And if you’ve ever done the QBank, you have the sharpe ratio down!
Thanks! And if you want a slightly lower return, you lend the RF asset? But in this instance cant you just take positions in two corner portfolios?
If there are restrictions against borrowing you’d use the 2 adjacent corner pf’s. No need to lend the RF I think.
Even with restrictions on borrowing you can combine the RF asset and the portfolio with the highest sharpe ratio to achieve a better risk/return portfolio than anywhere on the efficient frontier (other than the tangent portfolio). This is the CML. Borrowing at the RF allows you to go past the tangency portfolio (ie further right) on the CML. ETA: This is more of a L2 concept. I’ve definitely seen a focus on combinations of corner portfolios at L3, but I have seen this question a few times.
ok I might be wrong on this. but… shouldn’t any combination of the risk free asset and tangency portfolio have THE SAME RISK ADJUSTED RETURN. That is because the slope remains the same. All you are doing is changing the maximum return that can be achieved - but that implies increased/decreased risk ( depending how you move along the cml)
I agree with ozzy here. If your required return is BELOW the portfolio return with the highest Sharpe ratio then combine the highest Sharpe ratio portfolio with lending at the Rf. If you use adjacent corner portfolios here it will NOT be the optimal risk/return tradeoff. If the required return is ABOVE the highest Sharpe return and you can’t borrow on margin then you have to use the two adjacent corner portfolios that get the job done.
mwvt9 agree with what you said but strictly for a combination of rf asset and the tagency portfolio, wouldn’t their combinations have the same risk adjusted return? only some would have higher risk/higher return etc?
florinpop Wrote: ------------------------------------------------------- > mwvt9 agree with what you said > > but strictly for a combination of rf asset and the > tagency portfolio, wouldn’t their combinations > have the same risk adjusted return? only some > would have higher risk/higher return etc? That sounds right to me. They would all plot on the CML. In order to have higher risk adjusted returns that the market you have to plot above the CML so I think you are correct.
So going back to Philly’s question, the answer would be no and the main benefit of adding/shorting the RFR asset to a portfolio would be controlling the expected risk/return.
I think the answer would be yes. Because if you don’t have the Rf asset in the mix you can’t use the CML. That mean you have to use corner portfolios with a less than optimal Sharpe ratio. Edit: The risk free asset itself doesn’t do this, but the ability to combine the Rf with the optimal tangency portfolio does (vs just using corners).
Pop - I agree with most of what you are saying. The sharpe ratio obviously doesn’t change as you move along the CML, but you can achieve a higher return and the same risk as you move left down the CML (away from optimal tangent portfolio) compared to combinations of corner portfolios with lower sharpe ratios.
ozzy609 Wrote: ------------------------------------------------------- > Pop - I agree with most of what you are saying. > The sharpe ratio obviously doesn’t change as you > move along the CML, but you can achieve a higher > return and the same risk as you move left down the > CML (away from optimal tangent portfolio) compared > to combinations of corner portfolios with lower > sharpe ratios. Agree. As with any efficient frontier, you want to get into the northwest corner (high return, low risk). Because the CML plots above the frontier itself you are getting a better risk adjusted return. And of course you can’t get on the CML without the Rf.
I get you BUT the tangency portfolio by itself is a point on the CML( the allocation of 0% RFR and 100% tagency portfolio) OF course if you move anywhere ELSE on the curve(without adding rfr which would lead to cml) the portfolio on the curve would be dominated by the CML. - so you are right here. But the simple addition of the rfr to a tangency portfolio shouldn’t change the risk adjusted portfolio
I guess you could look at it that way… but, unless your required return is exactly what the tangency offers you are going to pay a price with lower risk adjusted return without the Rf.
I am not arguing that a combination of tangency portfolio & rfr is not beneficial, and that it would not be better than 2 corner portfolios. Agree 100%. but strictly to the question asked, the risk adjusted return would not change. The only thing it would allow you to do is adjust the portfolio to accepted risk or required return in optimal conditions
Agreed, doesn’t change as you move along CML. Only changes as you move from the non-optimal corner portfolio to the CML.
mwvt9 Wrote: ------------------------------------------------------- > I agree with ozzy here. > > If your required return is BELOW the portfolio > return with the highest Sharpe ratio then combine > the highest Sharpe ratio portfolio with lending at > the Rf. If you use adjacent corner portfolios > here it will NOT be the optimal risk/return > tradeoff. > > If the required return is ABOVE the highest Sharpe > return and you can’t borrow on margin then you > have to use the two adjacent corner portfolios > that get the job done. This sounds right to me. For risk levels below the tangent portfolio, you combine the tangent portfolio with the RFR. If you have a restriction against borrowing/levering, it doesn’t affect low risk portfolios (i.e. lower risk than the tangent portfolio), but if you want higher risk, you’d need to start moving along the efficient frontier (rather than the Capital Allocation Line). Also, I doubt they’d test this, but you’d have different tangency portfolios if your borrowing rate (where you pay for your credit risk) and your lending rate (which is RFR) are different. That would suggest that below one level of risk, you’d combine the low-risk tangent portfolio with the RFR, for very high levels of risk, you’d borrow and invest the proceeds in the high-risk tangent portfolio, and that for middle levels of risk, you’d move along the efficient frontier between the two tangent portfolios, changing your portfolio mix accordingly. I could be wrong, but I don’t think there’s any theorem saying that tangent portfolios are necessarily corner portfolios (though they could tell you to assume it on the problem). – As for terminology, remember that Capital Allocation Line (CAL) is the line through the RFR and the tangency portfolio. If the tangency portfolio is also the market portfolio, then the CAL is the same as the CML. If the tangency portfolio is not the market portfolio, the CML is still the line through the RFR and the market portfolio, but it is not necessarily the optimal set of portfolios (usually it’s a pretty good one, though). Generally, for CAL=CML, you need to 1) be able to invest in all assets (i.e. able to hold all assets in the market portfolio), and 2) believe CAPM (necessary for concluding that the market portfolio is the most efficient portfolio). There may be another theory that concludes that the market portfolio is necessarily the most efficient, but I think CAPM is the only one that asserts it strongly.