Suppose two portfolios A and B have an expected return of 10% each. But A’s risk is 8% while that of B is 12%. Looking at these two portfolios you would think, both give the same returns, but A has lower risk, I’ll buy A. But if you’re adventurous, you’d say portfolio A can return between 2% and 18%, while B can give between -2% and 22%. You might choose B. Portfolio B offers a chance of getting 22% return but there’s also the possibility that instead of making gains, you might end up losing money. The additional return is compensation for additional risk. Hence the notion, the higher the risk the higher the return. How do you make an optimal portfolio? By selecting the right combination of assets. If two assets are similar, then their prices will move in a similar pattern. Say, two Exchange Traded funds or ETFs from the same economic sector tend to show similar price movement, while, ETFs from different sectors show dissimilar price movements, as they lack correlation, making them a suitable set of eggs for your basket. Correlation is measured on a scale of -1 to +1. +1 indicates positive correlation where prices of two assets move par-for-par, while -1 shows negative correlation; prices move in opposite direction. If you put two assets with correlation of +1 in a portfolio, the risk they bring to portfolio will be the sum of the weighed risk of individual assets. However, if you put a pair of assets with correlation of less than 1, then the risk of the resulting portfolio will be less than the sum of the weighed risk of individual assets. By selecting different asset combinations you can achieve every risk to return combination in a portfolio. And this brings us to the efficient frontier, which is a graphical representation of different combinations of assets to achieve an optimal level of return at any given level of Risk. With risk on X-axis and return on Y-axis, this hyperbola shows all outcomes for various portfolio combinations of risky assets. This Straight Line is the Capital Allocation Line, which represents a portfolio of all risky assets and the risk-free asset, like government bonds. Tangency Portfolio is the point where the portfolio of risky assets meets the combination of risky and risk-free assets. And this portfolio maximizes return for a given level of risk. As you move towards the right along the lower part of the hyperbola you get lower returns at higher risk. Do the same along the upper part and you get higher returns at higher risk. The take away is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. We utilize Modern Portfolio Theory in our module 1, which has allowed us to achieve such returns…
I have so much respect for how a good explainer you are. This video is amazing. Very clear, structured and most importanty calm (good comfort for ones who find these processes taunting already).
In finance, the Markowitz model - put forward by Harry Markowitz in 1952 - is a portfolio optimization model; it assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. Here, by choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk. The HM model is also called mean-variance model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios. It is foundational to Modern portfolio theory.
3 года назад+1
MPT which is Modern Portfolio Theory considers how an investor should choose a portfolio with a good trade-off between risk and expected return. Markowitz showed that the set of possible expected returns and risks.
Portfolio management can be painful because it's all about making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, minimising risk while keeping good returns and balancing risk against performance and not everyone could handle this successfully. Ahmad did an excellent job in clarifying all concepts jointly.
Great lecture, well done! I do have a question, for the Lagrangian function, with only a handful stocks, it suggests negative weights. Is there a way to set a constraint for long only approach? Appreciated much.
The Markowitz solution can easily find highly leveraged portfolios (large long positions in a subset of investable assets financed by large short positions in another subset of assets)
The Efficient Frontier takes a portfolio of investments and optimizes the expected return in regards to the risk. That is to find the optimal return for a risk.
How to determine the optimal asset weights for a risky portfolio and how to allocate a portfolio between the optimal risky portfolio and the risk-free asset ?
As investopedia points out, it assumes that asset returns follow a normal distribution, but in reality returns can be more the 3 standard deviations away. Also, the theory builds upon that investors are rational in their investment, which is by most considered a flawed assumption, as more factors play into the investments.
Hi Ahmad. Just one question, if we get w = [0.2, 0.3, 0.4, 0.1], does that mean we have 20% in the first stock, 30% in the second, 40% in the third, and 10% in the final stock. It all sums up to 100% ? Thank you for awesome lecture.
The Markowitz Portfolio Theory is no other than a combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk usually proxied by the standard deviation of the portfolio's return
A portfolio that gives maximum return for a given risk, or minimum risk for given return is an efficient portfolio. Thus, portfolios are selected as follows:(a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and (b) From the portfolios that have the same risk level, an investor will prefer the portfolio with higher rate of return.
I always thought of Markowitz efficient frontier as a parabola where the optimal values lie along the upper half of the parabola line. Anyways, the Efficient Frontier gives you a way to balance your portfolio.
Portfolios that cluster to the right of the efficient frontier are also sub-optimal, because they have a higher level of risk for the defined rate of return
Please help with this problem I have homework An investor wants to put together a portfolio consisting of up to 5 stocks. Using the Markowitz method, what is the best combination of stocks to minimize risk for a given return? In this model, we calculate stock returns, the variance of each stock, and the covariances between stocks, using the Excel functions AVERAGE, VARP and COVAR.
Is it possible to have zero weight in a particular stock in Markowitz portfolio optimization ? Zero weight implies that nobody wants it which will actually lead to decrease in price, however it is not feasible.
It's an awesome video, but... Our optimization problem had constraint to have a better (at least the same) return than a minimum acceptable return. But in scipy minimization you set this constraint to target minimum acceptable return. Why? We should just use the "ineq" type as I remember. And therefore we (probably) would get another solution. And, as I understood, your linear equation makes a minimum return as a target too (sorry, 1 am, skipped some logic, sorry :( )
You have explained in less than 50 minutes what my lecturer struggled to explain in 3 months. Thank you!
This lecture slaps harder than my dads belt.
*The following content is created under an intellectual property license* Never have I ever seen such perfect and clear explanations.
ok
👍🏻
@Dave Frami *Please send me the IP license*
@aisha houra How did you put all outlines as clickable comments ?
Haha !
Wow now I can use your equation to do my own solver. Thanks.
I just did and it works perfectly
This lecture will make your pocket rocket 🚀
It sure did pocket made 5K USD yesterday thanks to this opt problem.
Mesmerizing insights and its for free!!.. Good job Ahmad !
I love the math flow starting at 06:40 Thanks a lot Ahmad !
00:00 Introduction
00:47 Markowitz Portfolio Optimization Problem (a recap)
03:08 Lagrangian Function
05:38 Optimal Weights
11:11 Lagrangian Multiplier Solutions
21:35 Our Portfolio Solver Equation
22:17 Python Implementation: SciPy approach (method 1)
33:36 Python Implementation: Our Solver (method 2)
37:28 Comparisons: SciPy Solver vs Our Solver
41:00 Summary
41:40 Outro
Very helpful
Funny. I understood most by a guy that does not look like people from Goldman Sachs
A true definition of a Guru
Ahmad is the best !
Better than any youtuber out here ❤️
Yes
Suppose two portfolios A and B have an expected return of 10% each. But A’s risk is 8% while that of B is 12%. Looking at these two portfolios you would think, both give the same returns, but A has lower risk, I’ll buy A. But if you’re adventurous, you’d say portfolio A can return between 2% and 18%, while B can give between -2% and 22%. You might choose B. Portfolio B offers a chance of getting 22% return but there’s also the possibility that instead of making gains, you might end up losing money. The additional return is compensation for additional risk. Hence the notion, the higher the risk the higher the return. How do you make an optimal portfolio? By selecting the right combination of assets. If two assets are similar, then their prices will move in a similar pattern. Say, two Exchange Traded funds or ETFs from the same economic sector tend to show similar price movement, while, ETFs from different sectors show dissimilar price movements, as they lack correlation, making them a suitable set of eggs for your basket. Correlation is measured on a scale of -1 to +1. +1 indicates positive correlation where prices of two assets move par-for-par, while -1 shows negative correlation; prices move in opposite direction. If you put two assets with correlation of +1 in a portfolio, the risk they bring to portfolio will be the sum of the weighed risk of individual assets. However, if you put a pair of assets with correlation of less than 1, then the risk of the resulting portfolio will be less than the sum of the weighed risk of individual assets. By selecting different asset combinations you can achieve every risk to return combination in a portfolio. And this brings us to the efficient frontier, which is a graphical representation of different combinations of assets to achieve an optimal level of return at any given level of Risk. With risk on X-axis and return on Y-axis, this hyperbola shows all outcomes for various portfolio combinations of risky assets. This Straight Line is the Capital Allocation Line, which represents a portfolio of all risky assets and the risk-free asset, like government bonds. Tangency Portfolio is the point where the portfolio of risky assets meets the combination of risky and risk-free assets. And this portfolio maximizes return for a given level of risk. As you move towards the right along the lower part of the hyperbola you get lower returns at higher risk. Do the same along the upper part and you get higher returns at higher risk. The take away is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. We utilize Modern Portfolio Theory in our module 1, which has allowed us to achieve such returns…
Some good argument I see
@@AhmadBazzi lol wow
Oh my GOSHHH. I am going to watch this so many times. Bravo. The illustrations, the simplicity, the speed of speech, the examples.
Wow glad you think so Belle !
This video sums up what took me about 4 years of gradual self learning to know in only 42 minutes!
Wow glad it did
Al Khawarizmi re-incarnated !
I have so much respect for how a good explainer you are. This video is amazing. Very clear, structured and most importanty calm (good comfort for ones who find these processes taunting already).
Wow, thank you!
Clear lecture. Disclaimer: No student debt was created during the watching of this video.
Your explanation makes it much easier to understand. Thanks
You are welcome!
I have never seen anybody teach so clearly
Oh wow, thanks Jerome !
In finance, the Markowitz model - put forward by Harry Markowitz in 1952 - is a portfolio optimization model; it assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. Here, by choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk. The HM model is also called mean-variance model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios. It is foundational to Modern portfolio theory.
MPT which is Modern Portfolio Theory considers how an investor should choose a portfolio with a good trade-off between risk and expected return. Markowitz showed that the set of possible expected returns and risks.
Correct
This man is amazing.. very knowledgeable & good at explaining. Well done RUclips for recommending me here.
I think one needs to be a genius in order to be able to explain such an incredibly complex thing in such a beautifully simple way.
Brilliantly articulated multiple concepts within limited time, Thank you.
Thanks alot sir I really do appreciate your help with this video, I started off in this market not seeing the results I expected
Glad it helped
you explained it as simple as possible.. thanks
You are welcome
A brilliant explanation of MPT. Wish I had come across this sooner. Thank you !
Glad it was helpful!
I swear I’ve learnt more during this quarantine than all the years I was in school 🙌🏽 I’m a new person now lol
Wow that is awesome. Keep up the RUclips learning Emily. RUclips is a very rich source where you could learn almost anything.
This was extremely helpful and needed. Thank you so much.
Oh my GOSHHH. I am going to watch this so many times
Portfolio management can be painful because it's all about making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, minimising risk while keeping good returns and balancing risk against performance and not everyone could handle this successfully. Ahmad did an excellent job in clarifying all concepts jointly.
Thank you very much Ahmad !
You are very welcome
Learnt more in this four lecture than in the 4 months in class ✌🏻
Definitely will add this to my playlist for later! 🤙
Awesome! Thank you!
Great lecture, well done! I do have a question, for the Lagrangian function, with only a handful stocks, it suggests negative weights. Is there a way to set a constraint for long only approach? Appreciated much.
Hi! I have also faced the same problem. Were you able to fix it?
Amazing video needs to be shown in universities thank you for the development of this video.
28:45 Thanks for showing me how to use scipy minimize function. Always had troubles with it.
This video is very clear!
Glad you think so!
AMAZING AHMAD !
YOU ARE DALE. !
I wish my Professors approach their lectures like this.
Lmfao mine as well they suck
Very nicely explained. Great !!!!
Glad you liked it!
The Markowitz solution can easily find highly leveraged portfolios (large long positions in a subset of investable assets financed by large short positions in another subset of assets)
Nice way of putting it
Your content is freaking awesome
I am happy that you find it awesome
Love the part about making money from mathematical Convex Optimization.
great teacher really helped, thanks
Glad it helped!
Wow! It should have been atleast 3 hours. Tuned me in like a netflix show.
Best lecture on planet earth
Интересно, спасибо за видео)
Интересная информация, благодарю за нее
The Efficient Frontier takes a portfolio of investments and optimizes the expected return in regards to the risk. That is to find the optimal return for a risk.
You're a boss. This video changed my life
Mine also
YEAH, QUARANTINE VIDSSSSSS 2021 !!
How to determine the optimal asset weights for a risky portfolio and how to allocate a portfolio between the optimal risky portfolio and the risk-free asset ?
It is the w vector derived and implemented in the video.
A solver using 7 lines of python code at 37:22 got me going nuts ! How did you do that Ahmad !?
As investopedia points out, it assumes that asset returns follow a normal distribution, but in reality returns can be more the 3 standard deviations away. Also, the theory builds upon that investors are rational in their investment, which is by most considered a flawed assumption, as more factors play into the investments.
Gem of a lecture thank you
Glad you think so, Gretta ! I'm very happy for you
I coded one myself, but for mutual funds. This would help if you extended this functionality for that cause.
It could definitely be extended and applied to hedge fund analysis.
Hi Ahmad. Just one question, if we get w = [0.2, 0.3, 0.4, 0.1], does that mean we have 20% in the first stock, 30% in the second, 40% in the third, and 10% in the final stock. It all sums up to 100% ? Thank you for awesome lecture.
An excellent video with useful information.
Brilliant explanation
Glad you think so!
Great lecture from UCLA USA
Thanks and welcome. Pleasure it is !
The Markowitz Portfolio Theory is no other than a combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk usually proxied by the standard deviation of the portfolio's return
VERY GOOD explanation...
Glad it was helpful!
Now I think I’d like to see a video on Gold’s role in “Deleveraging”
it was very helpful. Thanks a lot!
Glad to hear that!
Nice explanation, thanks for sharing
Thanks for watching!
Altyazılar için teşekkürler
thank you so much for this clear explanation
A portfolio that gives maximum return for a given risk, or minimum risk for given return is an efficient portfolio. Thus, portfolios are selected as follows:(a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and (b) From the portfolios that have the same risk level, an investor will prefer the portfolio with higher rate of return.
Great presentation skills.
Thanks for watching
Underrated GURU !
The lectures he gives are priceless
great! please upload more videos about portfolio theory
More to come!
Excellent professor!!!!!!!
You are a genius. Thank you sir.
Thanks Ahmad !
Anytime Dogan !
@Mallie Bayes, yes increasing
incredible! thank you
I always thought of Markowitz efficient frontier as a parabola where the optimal values lie along the upper half of the parabola line. Anyways, the Efficient Frontier gives you a way to balance your portfolio.
29:21 Wow, never knew we could model the cost function as a python function
Informative tutorial.
Glad you think so!
Portfolios that cluster to the right of the efficient frontier are also sub-optimal, because they have a higher level of risk for the defined rate of return
29:52 Sir, is the bounds necessary because it not part of the optimization problem.
Please help with this problem I have homework An investor wants to put together a portfolio consisting of up to 5 stocks. Using the Markowitz method, what is the best combination of stocks to minimize risk for a given return? In this model, we calculate stock returns, the variance of each stock, and the covariances between stocks, using the Excel functions AVERAGE, VARP and COVAR.
Is it possible to have zero weight in a particular stock in Markowitz portfolio optimization ? Zero weight implies that nobody wants it which will actually lead to decrease in price, however it is not feasible.
How do you work out the optimization problem using Langrange?
It's an awesome video, but... Our optimization problem had constraint to have a better (at least the same) return than a minimum acceptable return. But in scipy minimization you set this constraint to target minimum acceptable return. Why? We should just use the "ineq" type as I remember. And therefore we (probably) would get another solution. And, as I understood, your linear equation makes a minimum return as a target too (sorry, 1 am, skipped some logic, sorry :( )
Thanks for the video.
You bet
I wonder what the Portfolio risk formula will be if there are a million number of stocks in the portfolio.
Yes the problem would be the inversion of the Sigma matrix. It would be too slow depending on the machine.
Superb.. thnk you Sir :)
So nice of you
love your videos! keep it up:)
Thank you! Will do!
awesome quality useful content
What are the requisites to study CFA?
Nice handwriting I see it has improved compared to your last tutorials.
agreed
Thanks a-lot sir I really do appreciate your help with this video
2:33 How is minimum accepted return an input to the problem ?
why rmin is 0.02 we expected it is some kind of dollars
Very clear, thank you so much :-)
Well done 👍🏻
Thanks for the visit
Is the CAGR true that CAGR = (end-price/start-price)^(1/years) - 1 ?
2:04 relative price changes are ratio of current period vs previous one ?
fantastic video !
Well done boss. 💪🏻