Capital market line (CML) versus security market line (SML), FRM T1-8

[@lusee2707]

The best video I've seen so far. And I have seen them all :-) Thank you

[@bionicturtle]

Thank you for the kind words (we aim for quality)!

[@alexh.4842]

Agree. I'm prepping for CFA level 2, and still come back for this level 1 concept. Thanks Bionic for explaining it so well.

[@Aviate213]

you explained it in such a succinct and clear way. Thank you!

[@OsvaldoCM97]

Excellent way to do a brief analysis on the relevant differences, thank you

[@LyAn215]

Hi. Can you explain to me why the Sharpe ratio does not change in accordance with the weight of risk free assets as you said at 6:44? Thank you very much.

[@bionicturtle]

Hi Ly An, Because the ASSUMPTION is that we stay on the CML as we add/subtract the riskfree asset, and the slope of a straight line is the same at every point on the line. The slope of the SML is the Sharpe ratio of Market Portfolio: I like to recall that slope is just rise/run. Pick any point on the CML and the "rise" (the vertical distance from the RISK-FREE rate, which is on the Y-intercept) is the EXCESS return, while the "run" (horizontal distance from the Y-axis is the standard deviation, σ. So hopefully, you can "see" how the slope of any point on the blue (CML) line must be = (excess return)/σ? Well, that's the market's Sharpe ratio. Hence, every point on the (straight!) CML has the same (market's) Sharpe ratio. And our simplifying assumption (under the unrealistic CAPM) is that adding/subtracting riskfree asset can only move up along the line (Why? Because we assume the allocation can only be between the two assets: the riskfree rate, and the optimal Market Portfolio of risky assets). I hope that's helpful!

[@LyAn215]

Bionic Turtle No one could’ve explained that better than you :) Thank you very much.

[@delbroox]

Best video on the Subject. Thank you very much.

[@bionicturtle]

Thanks so much! We appreciate you watching!

[@TINAROBERTS7]

Wow. So neatly explained. Thank you very much!

[@samchan427]

Hi, it is the best video in this topic I saw it too. You made the simplest way to understand these concepts. Thanks 😊

[@user-st6is9ml4x]

9:05 How to calculate Rm? Rm= w1*A1 + w2*A2 ??

[@Tyokok]

8:45 does any one know how to introduce the correlation into the formula? Thank you!

[@young959]

Thank you so much, this video gives me clear answer for the question that seriously confused me

[@sssharma38]

Excellent explanation

[@katherineli3435]

Awesome video, really helpful! Thx a lot!!!

[@bionicturtle]

glad to hear it's helpful, thank you!

[@howwtoacademy]

How to calculate volatility of a portfolio with the volatility of Individual stocks given the asset allocation of stocks in the respective portfolio !!

[@dbsk06]

where is the excel for this please? thanks for the tutorial

[@peteranton6951]

Correct me if I am wrong, but if you look at the CML line and you make the distribution from 0 t o100% percent of rf asset vs market portfolio, you end up on the line between the y-axis and the market portfolio. how do I create a portfolio which is right hand side of the marketportfolio but on the clm?

[@peteranton6951]

.

[@samhayman8933]

I was wondering the same thing. My lecturer said something about borrowing but I didn't understand. At the y intercept, 100% of allocation is in the Rf rate At the market portfolio, 100% of the allocation is in the risky assets (0% in Rf rate) So how are point on the CML attainable to the right of the market portfolio?

[@thomasnguyen2438]

Wow this video is amazin thank you so much!!

[@cecilia3824]

What does the portion of the convex curve with high volatility and returns below the risk free rate represent. Do those portfolios exist under the theoretical framework?

[@harshitashetty5513]

Thank u so much sir☺️

[@ScRaS181]

How do you get beyond the market portfolio on the CML? How can you allocate more than 100% to the market portfolio?

[@bionicturtle]

You BORROW at the risk-free rate, which leverages the return. There is a continuum from investing your entire amount in the risk-free rate, to increasing the allocation to the market portfolio, until you have zero in the risk-free asset and then, beyond that instead of investing at the risk-free rate, you switch to borrowing at the risk-free rate which is leveraging the market portfolio

[@ScRaS181]

@@bionicturtle Thank-you! This makes sense.

[@MA-yz7ef]

Thank you!

[@dipanjandash4485]

thank you. very good and lucid explanation.

[@fndTenorio]

Suppose I trade in a market with 1000 stocks total, then I select 10 stocks and optimize for the highest sharpe ratio portfolio. Now in the case of SML, what is "the market"? My 10 stocks or the entire market of 1000 stocks? Can you clarify on this? thank you!

[@xingjiande7631]

Thank you very much, it helped me so much!

[@emanuelemontillo6329]

Hello thanks for the video, i have one question: the SML includes only securities or even portfolios? If yes, why in the SML (if we consider it with the securities investment) there is anyway the market portfolio for beta=1?? I

[@aitorjara100]

Hi professor, I found this question on a mock exam and while it is intuitive that there is a diminishing ratio of return to volatility because of the concavity of the efficient frontier it doesn't make sense to me that the Sharpe ratio then keeps increasing from the minimum variance portfolio until the optimal portfolio. Please, see the question: Q. As one moves to the right along an investor’s efficient frontier, a set increase in risk is most likely to lead to: A) sequentially smaller increases in expected return. B) consistent increases in expected return. C) sequentially larger increases in expected return. Answer is A. Why sharpe ratio gets higher while we approach the optimal portfolio, then? If I follow my intuition I answer A, If I follow the logic of the Sharpe ratio I answer C Thank you, a lot !

[@teerificbitch]

A. Garcia?

[@aitorjara100]

Dude Trust Me Is that supposed to be a question?

[@aspiringmodernistchef]

I think you are confused. Sharpe ratio is not actually a measure of the gradient. If you look carefully, the denominator of Sharpe ratio is the portfolio risk at that point and not change in portfolio risk, so it's measuring an average. On the other hand, think of the gradient at any point as the marginal return of risk. So on the left of the optimal portfolio, the gradient is steeper but note that this is marginal. So if marginal is higher than the average, then it increases the average, which is the Sharpe ratio. Past that point, it adds marginally lesser per unit risk increase, and so Sharpe ratio would fall. I hope that answers your question.

[@user-st6is9ml4x]

@@aspiringmodernistchef isn't it something like this? SR= ( Rm - Rf )/(var M - var f) And variance of risk free asset is 0, so = (Rm - Rf)/var M ? If so, isn't it change?

[@jinomaster]

Thank you, very useful.

[@bionicturtle]

Thank you for watching!

[@hilolaniyazova1919]

Dear Sir, If the volatility of P is 11.2% and what is the Beta of M? Thank you

[@bionicturtle]

Hi Hilola, The beta of the market portfolio, β(M), is assumed to be 1.0 (or approximately 1.0) because we are referring to the beta of the market with respect to itself. I think you edited your prior question? The key relationship is that the beta of the portfolio with respect to the market, β(P,M) = covariance(P,M)/variance(M) = [correlation(P,M)*volatility(P)*volatility(M)]/variance(M); cancel volatility(M) and we have β(P,M) = correlation(P,M)*volatility(M)/volatility(P). Symbolically, β(P,M) = ρ(P,M)*[σ(M)/σ(P)], so that we can say "beta equals correlation multiplied by (aka, scaled by) cross-volatility. (aka, ratio of volatilities)." I hope that helps!

[@bratan_archer]

@@bionicturtle Thanks for clarification ! Wondering why is it volatilityM/volatilityP, not the other way around ? Thanks.

[@SuperBratkov]

hey great tutorial. I have a question, if the SML accepts all portfolios, how do you know which one is the efficient one? is it the same theory which you use for the efficiency frontier and the CML?

[@fndTenorio]

It is located where beta = 1.

[@No_BS_policy]

If beta =1, sharpe ratio is at the highest i.e. the CML.. if beta1, the portfolio is no longer efficient as it no longer contains the market portfolio where sharpe ratio is at its highest

[@rainerfs4563]

Thanks for the video. I am curious about how did you get the standard deviation of the portfolio. The only formula I know is that: sqrt(wa2.deva2+wb2.devb2+2.wa.wb.covab). I calculated in your example and it is different. Appreciate any comment

[@znanyun]

I applied the same formula as you wrote here to the numbers in the video and got exact the same standard deviation as listed in the example. You might want to double check your calculation.

[@Fudelover]

This is confusing. Whats the difference between the SML and and portfolio possibilities curve if both are configuring asset allocation between A and B?

[@bionicturtle]

The difference is the x axis: the PPC plots E(return) against volatility (total risk), but the SML plots E(return) against beta (systematic risk). In my example above, the various risky-only portfolios will indeed map between the two; i.e., the PPC implies a corresponding SML if you swap the X axis, and vice-versa. This "works" because both lines will contain any and all mix of risky-only assets, in CONTRAST to the CML which is efficient and will not contain most of those portfolios (the CML only contains a mix of the riskless asset and the optimal market portfolio, wo while any of the points on the CML will map to points on either the SML or the PPC, the inverse is not true. Most of the points on the SML/PPC will not map to the CML as they have lower Sharpe ratios). Less confusing now, I hope? ;)

[@Fudelover]

Thank you for replying! I think most of my confusion lies in the difference between expected risk (standard deviation or returns of the market portfolio) and Beta (systematic risk). Are we saying expected risk refers to a single portfolio risk and beta refers to the relationship between the risk of the single portfolio and every other possible market portfolio?

[@bionicturtle]

The beta in SML is always systematic risk (per the definition of CAPM), so the SML is a plot of a security (or portfolio's) expected return against beta of the security with respect to the Market portfolio which is the optimal portfolio (i,e, portfolio with the highest Sharpe ratio on the PPC curve). That's why I always denote beat with β(p,M) to emphasize "with respect to the Market portfolio." For PPC/CML, they plot a straightforward expected return against standard deviation. In a simple 2-asset example (as above) a confusion can arise because in the SML we are plotting a portfolio that happens to mix A & B (because it's super simple and we only use these assets!) against beta "with respect to an optimal portfolio" which is also a mix of A & B (but, again, we could put anything on the SML, it only cares about the portfolio's beta). I hope that helps.

[@drockccc5633]

Hi, why SML model seems exactly same as CAPM model? Are those actually same things? Thanks

[@alexkingcoopers]

yeah its a visual representation of CAPM

[@bionicturtle]

I agree with Alex. What I've said in our forum is: "SML manifests the CAPM, such that in practice--i.e., E[excess return] = priceRisk*quantityRisk--they are used interchangebly. SML is the line; CAPM is the broader theory and set of unrealistic assumptions that produces the SML but includes *ideas* like the all-important Equilibrium; SML/CAPM has systemic risk (beta) on the X-axis. CML is the efficient frontier after the riskfree asset has been added to the minimum variance portfolios (the curvy line), of which the most important risky (i.e., all risk assets) is the Market portfolio (b/c it has the highest sharpe ratio). CML has total risk (volatility) on the X-axis."

[@aitorjara100]

I'm confused with some of the notation... if the linear equation reads n + mx, being n the intercept (rf) and m the slope, wouldn't the slope be excess return E(r) - rf (change in y axis) divided by standard deviation of the portfolio (change in x axis) ???? I'm confused because you say it's standard deviation of market, which makes the sharpe ratio, and then multiplies by the standard deviation of the portfolio. Jesus christ.. I will never understand all this !! Also on a parallel process, what does exactly mean that the CML is above the efficient frontier once it surpasses the tangency point in real life? Does it mean there is a combination of the risk free asset and the market portfolio (risky assets) that makes me earn more than if I just invested all my capital in the risky assets, which always plot on the efficient frontier?? Thanks a lot for your help !

[@bionicturtle]

I don't say anywhere that slope is σ(m). Listen at 7:00 The slope of the CML is [R(m) - rf]/σ(M), which is the Sharpe ratio of the market portfolio. Additionally, all points on the (efficient) CML have the SAME Sharpe ratio as the market portfolio; i.e., different portfolios will have Sharpe ratios given by [R(P) - rf]/σ(P), but in my example, these will all be the same S = 0.671. In summary, the CML is the line of the most efficient portfolios (i.e., the portfolios which all offer the same and highest Sharpe ratio), INCLUDING the market portfolio, and given that the X-axis is portfolio volatility, this common Sharpe ratio is also the slope of the CML (and will be higher than any of the "less efficient" portfolios BELOW the CML) . Thanks,

[@aitorjara100]

Yes, I didn't express myself correctly, I wanted to say "because you divide by the standard deviation of the market, instead of the standard deviation of the portfolio". I know the formula is like that but I was having a hard time trying to understand because the point of my confusion arised from the x axis variable being measured in σ(P) in the graph, so I wasn't getting why we had a σ(m) on the denominator . Mathematically speaking I get the slope like this -->"rise over run". That's why i didn't understand it. So far I think I understand the key point which is that all the portfolios that plot on the CML, because of adding them the risk free rate, are the most efficient ones being that all of them have a direct linear relationship between total risk (σ) and excess return, unlike the efficient frontier which is not linear but convex, because of diminishing excess return over total risk (diminishing sharpe ratio) for σ's higher than that of the optimal portfolio. If that is correct I think I'm getting it. The other question is, when you talk about the allocation between the rf and risky assets you show the exact same sharpe ratio. Is it correct to state that despite the sharpe ratio being the same I assume more risk by investing less in the risk free asset and more in the market portfolio despite I am being rewarded for that additional risk ? (rewarded because market portfolio only has systematic risk (non diversifyable risk, B) ). Also, is it borrowing at the free risk rate and investing everything to the market portfolio (0% to the rf and 125% to the risky assets for example) the situation in which we are in a point of the CML where σ is bigger than 0.11? ( above the purple triangle) and in that case, thus, would the sharpe be the same but with higher σ ? Thank you a lot and sorry for the huge paragraph, and for my english. I just found your video is awesome because I flew over this topic and thank god I had the chance to actually understand this rather than memorising it. I have the CFA level 1 in 13 days.... I will kill myself if I don't pass this haha

[@mikekahne1872]

why are you using 6% when treasuries are much lower

[@bionicturtle]

I selected the assumptions to make the chart easier to follow (as I often do); e.g., RF rate might be unrealistically high so the blue callout doesn't block the x-axis. I often exaggerate and/or round assumptions if i think it helps improve clarity. You'd be amazed at the little details involved when you go to video. Thanks!

[@aitorjara100]

You realise this is just a showcase of the actual concept right? it's not an hypothesis of what the actual values should look like..... Some of you guys just like moaning for no reason

[@kamarireynolds6349]

does anyone have Sir Reed Cooper details i want to start an investment with him

[@richsherrard7124]

you know about Mr Reed Cooper ? i guess he has helped a lot of traders