Hey Guys, A 100% diversified portfolio under the assumed conditions, would eliminate all unsystematic risk, right? Now would this portfolio yield the same as a T-Bill?
I would say no because a T-Bill is just one security verus your portfolio that consists of mutiple assets. If you were comparing your portfolio to a portfolio of T-Bills I would still say no because the systemic risks would be different between the two portfolios. It all depends on how much of the unsystematic risk you were able to diversify away. So, the yield will depend on your market risk and for a portfolio of diversified assets to yield the same as a portfolio of T-Bill you would have to chose and allocate your assets to mimic the T-Bill portfolio’s return as a benchmark. Just my thoughts.
A quick correction, I didn’t notice that you said 100% diversified. If a portfolio is 100 diversified, then we have diversified virtually all of the unsystematic risk (from my understanding there is a small amount of systemic risk still present); but, the portfolio will not yield the risk free rate because the unsystematic risk profiles between the two portfolios are still different. i.e. I could have a perfectly diversified portfolio that included LEH, Fannie, Freddie and BEAR assets; but, their unsystematic risk profiles still made them more risky than a portfolio of T-Bills. Unsystematic risk is the firm or industry specific risk. T-Bills are backed by the full faith and credit of the United States Government, which is why they are considered to be risk-free. Naturally, any security or portoflio of securities that are not risk-free (risky assets) should require a higher yield than a portfolio of non-risky assets.
Me1999, I mostly agree, but one minor correction/nitpick: “If a portfolio is 100 diversified, then we have diversified virtually all of the unsystematic risk” If it is 100% diversified, there is, by definition, no unsystematic risk. And if only systematic risk remains, does that mean that any systematic risk (i.e. macro-economic variables - money supply, interest rates.) will affect expected return of the M portfolio to the same extent as the T-Bill? hmmmm My inclination is the answer is maybe, and it is dependent soley on where you are on the capital market line, which is based on your decision of how leveraged you are. But, your risk adjusted returns would be the same as the T-Bill’s risk adjusted returns.
You have a well-diversified portfolio that has systematic risk and RFR that has no risk (supposedly). Therefore, since well-diversified portfolio has higher risk than risk-free instruments, it has a risk premium return component.
But doesn’t the risk free component just refer to the nominal return and default risk? There is still potential liquidity risks (unlikely with treasuries of course, but we are talking theoretically) as well as an inflation risk. Or does the risk free security in this discussion mean that literally?? My assumption was that it was some sort of government security and not a theoretically risk free note of some kind, but I could well be wrong.
I assume we are discussing why market portfolio theoretically yields higher return than risk free rate of return. >A 100% diversified portfolio under the assumed conditions, would eliminate all >unsystematic risk, right? Now would this portfolio yield the same as a T-Bill? My answer above is: market portfolio still has systematic risk whereas RFR doesn’t.
“My answer above is: market portfolio still has systematic risk whereas RFR doesn’t.” If this were true then Treasury securities would be immune to changes in interest rates. Since the duration of Treasury securities does not equal zero then we can conclude that they have some form of systematic risk associated with them. So, a portfolio of Treasuries yielding the RFR will have systematic risk.
I think Maratikus is correct, IF we are talking about a theoretical completely risk free security. As I read the text I had assumed that by “risk free security” they had meant a treasury, which of course carries some systematic risk. However, based on this discussion, and the fact that the whole M portfolio is theoretical, I see that it may also be prudent to presume that the risk free security is also theoretical. After all, the text never refers to it specifically as a US Treasury or anything.
I like your conclusion, Chi Paul.
They do want u to assume tho that the treasury security is the risk-free rate they are talking about.
“They do want u to assume tho that the treasury security is the risk-free rate they are talking about.” That’s what I thought as well. I believe the risk-free rate is always assumed to come from the Treasury securities–at least in market practice and in academia. The Treasury is the risk-free security because it is theoretically free from default risk due to it’s backing by the full faith and credit of the U.S. government. So, we assume that the security is risk-free because we should be confident that we can hold it for its entire life and receive our principal at maturity plus all coupon payments during the life of the security.
True RFR exists only in theory, practioners use US treasury instruments (T-bill for short-term, and T-bonds for long-term) depending on the situation. In our discussion we mix those two together.
Thanks guys, yeah i over looked the risk premium. Got it now.