16. Portfolio Management

MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
View the complete course: ocw.mit.edu/18-S096F13
Instructor: Jake Xia
This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@DoneDifferently]

Clear and informative lecture. Disclaimer: No student debt was created during the watching of this video. Thanks MIT

[@Rxzwell]

well they failed to mention the best investment in history "blockchain"

[@carriermodulation]

But you also don't get the degree that lets you get his job at Morgan Stanley.

[@eitkoml]

Correction, some student debt was created as there were tuition-paying students in that room during that lecture.

[@reginald8623]

Would that dude be saying shit if he wasn't getting .013% of the criminal amount of money people pay? supply and demand, or i demand your compliance or you will be ruined.

[@meenasuman6917]

@@carriermodulation what u say today o will try but give me good brifing beforehand गमे start thanks

[@omgyeaXD]

Pretty decent world we live in right now. I can learn all this for free.

[@japhasonlauren9925]

you can only appreciate a person who tries to teach everyone how to invest and invest and make profits on multiple ways, up and down

[@futurnekedesin9172]

it's crystal clear why most us lavish in investment lost due to ignorance

[@futurnekedesin9172]

Thanks for the wonderful wonderful info

[@manfredholzkopf9522]

not for free, you are investing your time

[@shouryaseth5715]

@@user-cd6ny9yp9y hey would you recommend any books or research websites online for young people who want to get into investing?

[@EnglishLerner0]

03:05 Starts 05:37 Steps 11:05 Instruments 13:54 Portfolio goals 19:16 Portfolio goals | What is risk? 21:11 Expected return 22:33 Expected return | Instruments 26:33 Expected return | Efficient frontier 27:54 Expected return | Efficient frontier | How to find it? 28:53 Expected return | Special cases with two assets 29:49 Expected return | Special cases with two assets | Case 1 31:40 Expected return | Special cases with two assets | Case 2 34:28 Expected return | Special cases with two assets | Case 3 34:54 Expected return | Special cases with two assets | Case 4 35:53 Expected return | Special cases with two assets | Case 5 39:50 Expected return | Special cases with two assets | Case 6 40:44 Expected return | Special cases with two assets | Case 7 41:22 Expected return | Special cases with three assets 43:09 Expected return | Beta and sharpe ratio 46:59 Portfolio allocation 51:26 Portfolio allocation | Diversification 56:22 Risk parity 01:00:15 Risk parity | Sharpe ratio

[@justingt3rs]

Thanks :)

[@217PARADISE]

what a champ

[@stat8715]

not all hero wear cap

[@no_more_spamplease5121]

35:53 = Case 5 (cash as a part of the portfolio) is very insightful.

[@no_more_spamplease5121]

50:27 = Nice explanation of the benefit of adopting risk parity + periodic rebalancing, with an example of scenario having 2 perfectly negatively correlated assets which are up 50% of the years each.

[@PullingEnterprises]

27:50 Efficient Frontier Kelly's Formula 45:30 Risk Parity: 59:30 1:16:00 forecasting by looking at only historical data is like driving and only looking in the rearview mirror

[@soccerplayer2277]

Using historical data and statistics helps understand the risk and the market's sentiment regarding a stock during certain times. The only way to look forward is considering the company's strategy and truly understanding its currently available resources. I work on a hedging team which is basically portfolio management and I would never use any of the hardcore math I've learned to select a single stock.

[@kylelarson5074]

@@soccerplayer2277 he is using the formula to figure out a diversification strategy based on SD and Ro of previously selected assets. Are you paying attention?

[@soccerplayer2277]

@@kylelarson5074 I was and I am fundamentally disagreeing with him. It is not a forecast, these statistics are estimators and are just being assumed to carry forward into the future. Rho is not a bad estimator for some purposes but implied volatility proves much better than SD of historical prices as it is usually based on the market's forecasts of the stock. Volatility during these past 2 years has been through the roof, partially due to trade conflicts and the expanding global economy. Would I use these historical volatility estimates to develop a portfolio for the next 2 years, where trade agreements are likely settled and the global economy possibly begins contracting? No. What I would do is forecast stocks individually, select all my assets and then determine the optimal weightings of the assets to produce the largest sharpe ratio of the portfolio.

[@DanOneOne]

I am so glad that I didn't pay for this course...

[@edimoh2822]

Markowitz

[@concepciongonzalez161]

I like Dr. Jake Xia. He explains so well and with a peaceful attitude. He looks genuine interest in the learning of the students.

[@paradigmshift2223]

Almost ASMR like lol. Seems like a super nice approachable guy.

[@wisconsinfarmer4742]

one thing about all of the MIT lectures, they seem so kind as individuals.

[@qrcdd8374]

Come for my country all professors are just sadist

[@NickByers-og9cx]

Ahh yes of course, diversify your GameStop with both stocks as well as options 🤔

[@Anonymous-wy5dc]

Doge go brr

[@rigzyded5911]

It’s a very important thing to diversify for us apes, you see when you have both calls and shares it reduces the chance of it going tits up.

[@PoleReseal]

I just like the stock

[@roger_rogers]

LEAPS as well as Weeklies

[@maadaaraa9344]

Stonks

[@nelsoncheetube]

Sincere appreciation to MIT for Sharing this lecture. I have never been to university but now I am able to learn from the greatest minds from your channel. Thank you 🙏

[@AstorSkywalker]

This is so cool, I could never afford going to MIT, I live in a third world country Honduras. But I wish I could get this type of high quality education

[@thesnackbandit]

@@AstorSkywalkerMIT is one of the least expensive colleges in all of America. If you are talented and have displayed it creatively and academically, the cost is almost free.

[@jcpettit1028]

I'd have loved to study under this professor. He asks his students what kind of approach they'd like and then adjusts his lectures accordingly.

[@Musikmaker658]

Talking as if the students show enough initiative to actually make something out of that offer. There are two sides to a coin.

[@jkholtgreve]

@@Musikmaker658 This is MIT not Harvard so he at least has a fighting chance with them :)

[@chesstictacs3107]

The dude has degrees in electrical engineering and computer science, and on top of all these, he knows the finance. Just wow.

[@eben3357]

Brilliant with numbers but misspelled, or perhaps it was the student who wrote the notes, commodities at 8:47.

[@marcusryden6732]

Asian power.

[@Fractal_32]

Diversification should not only apply to financials after all. A greater diversification of skills and people should lead to a more stable society, “echo chambers” are not good or useful for a society.

[@stephanieposcablo2305]

@@Fractal_32 Been thinking the same thing regarding diversification throughout the lecture.

[@TheSystemaSystem]

@@eben3357 Second language, or perhaps third. I think we could allow him a misspelling

[@maximtsai1856]

Rest in peace that one guy who invested everything into Yahoo.

[@doppleganger3496]

YEAH, QUARANTINE VIDSSSSSS 2020 BABY YEAHHHH!!

[@user-vx2pw3ov4n]

u r not alone bro lol

[@lfernandods]

Hi from Brazil Quarentine..

[@doppleganger3496]

Luis Fernando Silva oi! Todo bom?

[@ayamisdelicious3600]

Lol

[@fabiobeccari8461]

Here I'm dude, from Italy

[@ryzarabino]

1. Understand your goals 17:02 University Endowment 17:33 Pension Fund - What is timeframe when workers retire and need to draw from the pension? 2. Be clear about how much risk you can take 19:20 What is risk? 26:08 Risk-reward investment map 27:50 Efficient Frontier 3. Building a Model 47:45 Plotting portfolio allocation 50:34 Risk Parity

[@mandex3570]

He smiles like *The Big Short* hedge fund manager

[@muabyt7333]

Great movie

[@kevinassang3158]

i think it's the same guy

[@GoodComedian2011]

Synthetic CDO manager?:)

[@young_speculator9144]

SYNTHETIC CDOs

[@thecapone45]

I literally thought the same thing before I even scrolled down to the comments!

[@arunanzogbia8972]

Thank you very much MIT for sharing this knowledge. Jake Xia, excellent teaching.

[@SuperGGLOL]

For some reason, i find it satisfying when he draws the graphs. he is a good graph drawer

[@stlouisix3]

Thank you for your amazing content MIT & thanks to Jake for his interesting lectures too!!!

[@MrAntonNelson]

He is such a cheerful person! He just can't help smiling all the time can he?))))

[@SFW7]

Thank you so much for providing this invaluable value to aspiring minds. This is the greatest service to humanity. The Professor is such an excellent teacher and it is amazing that we can listen to him from any part of the world. Many thanks, MIT and Prof.

[@royreyes8422]

this is how u stay alive across markets... great video with replay value. should be watched during this greater bull run as the most dangerous levels everyone is blind....

[@valeriybelozerov5309]

I appreciate you making complex trading concepts clear and accessible to everyone. Thanks for your valuable work!

[@tantran1995]

This professor is amazing

[@tensevo]

well - he is a real professional teacher.

[@muabyt7333]

Thats the difference between normal universities and top 20 universities.

[@wodroi]

very handsome ,i like the way he talks

[@LifeCoach44]

Andrew H did you miss the part where he explained why? Different people have different investment goals e.g. protection to principal before retirement

[@LifeCoach44]

Andrew H it was shortly after he said his portfolio was conservative. He reference back to the life stage graph and said something to the effect of, his main goal right now In his stage is protecting principal

[@farshadnoravesh]

The professor is very smart and nice because he wants to show that causality is missing in classical portfolio optimization and even in risk parity paradigm. beautiful video.

[@Anomander888]

Excellent lecture young man . You've expanded my old brain.

[@balan1983]

Thank you for the amazing lecture. Not fortunate enough to enroll in MIT but grateful to learn from this vid.

[@SuperRoycethe59]

great teacher really helped, thanks

[@mikek7396]

My portfolio: 100 SPY PUTS - expiry this friday - strike price $200

[@Tahiki6]

Mike K positions or ban

[@youngbungalo6874]

@@Tahiki6 How about positions and ban?

[@NikoLetubeur]

THIS IS THE WAY

[@Timtimzi]

lmaooo. goes to show that the stuff they teach us in finance classes just get thrown out the window.

[@seanlow2033]

Oh gawd - is no place safe from /r/wallstreetbets???

[@gonzalogonzalez7064]

I really like this MIT online self-learning education model, with good lighting and powerful lectures.

[@ken8844]

I really love MIT chalkboard. It seems so smooth and nostalgic.

[@shivanshkrishna9626]

In such an easy way he teaches difficult concepts

[@Xilladan093]

u have no muscle.. lol

[@shivanshkrishna9626]

I will try to build, thanks David

[@carrtyrone]

Best lecture on finance and intuitive thought process

[@AM-ux3yx]

I work in a front office investment control desk for one of Europe's largest asset managers. Found this very interesting, normally what you find is a degree of variance from the benchmark within equities, even then internal house rules will dictate only a minimal degree of variance. You'll find a lot of portfolios with have buckets for different asset classes (depending on the mandate), in particular, money market to sweep up excess cash to put the money to work whilst the PM picks securities. This presentation is really covering MAI funds. Great video and fantastic lecturer.

[@FinancialFaiz]

This is excellent. And its all for free!

[@zephheine9681]

shhh might start charging lol

[@erikeberhard8220]

Thank you for the brilliant content, this and the other, lectures are priceless. Knowledge is power!

[@user-wp4fg3kx7f]

Definitely mindblowing.

[@UpendraSingh-ti9ho]

You guys are doing excellent work in the world.

[@Dan1418]

I was lucky enough to sit in this class. MIT is the best place in my life.

[@SebastianRodriguez-hk2ji]

how do you feel now knowing you can just yolo half your net worth into weekly spy calls and it will probably beat anything these strategies can produce in 10 years lmao

[@latslarsson2001]

@@SebastianRodriguez-hk2ji you're trolling btw

[@swagger1930]

@@SebastianRodriguez-hk2ji and lose it all the next week 😂

[@poloska9471]

@@SebastianRodriguez-hk2jiI’d say this would be a hard “nope” for me as a professional trader for one obvious reason: it is a fact that on a daily basis, the relationship between the S&P closing up or down for the day is 50/50… so 50% of the time the market closes up, and 50% of the time it closes down… even in a modest bullish trend… given this knowledge, yoloing your net worth on SPY calls is NOT a good idea because the overwhelming odds are that you very well may be the one sad bastard who bought/sold them when the SPY decides for whatever reason that it wants to make a little pullback from which it will then take 2 months to recover from. Happens all the time… often enough for me to make a great living lol (I trade ES futures). Writing this on November 23rd, 2023, after the S&P posted one of the craziest rallies ever recorded. Straight line up, no downwards action - 14 green days with only 3 tiny little wicky red days… after a month when people thought Black Monday was going to repeat itself… now I’m sure more than a few people yolod the SPY puts that week before we began this rally and they most likely lost everything they had in their account, and some likely lost even more than they had… so… that’s my 2 cents on this strategy. Keep the yoloing strictly for Wall St Bets degeneracy.

[@Alexamdern]

haha, "the closest thing to a free lunch in investment.. is diversification". Im sure he came up with that on the stop. Great lecturer!

[@MRF77]

*...on the spot*

[@wallopwallop9125]

Lejonet nope he didn’t. It was ray dalio

[@matthewbryant2972]

This is not meant to be insulting... but this guy's voice is so calming, he could distribute these lectures and brand them as "Economy Lessons to put your restless mind at ease". This is like a sleep aid... it's awesome. I will be a master of Modern Portfolio theory in a decade.

[@YourHyness]

Definitely! Gonna add this one to my playlist for later! 🤙💯

[@micahwright1578]

He said that math is super simple and my mind over here is mind blown.

[@ofwbbbuhayko8335]

This professor Very excellent and thank you for sharing your knowledge god blesse Sir

[@arrowb3408]

At1:08:20 for these two examples, love it and easily understand. Learn a lot from this class.

[@inner_melodies]

"The closest thing to a free lunch in investment is diversification" - Jake Xia, 2013

[@bernardting3361]

Excellent analysis Very clear concepts It makes me understand the theme of finance and applications Many thanks

[@kafimahmud2144]

This lecture helped me understand few terms very clearly

[@erichkraetz2622]

excellent professor, thanks for sharing

[@TamirlanGurbanov]

Thanks a lot dear Dr. Jake Xia !

[@troy2923]

Thankyou very much Jake and MIT OCW, brilliant applications and formulas, great lecture

[@cheriew4385]

the clarity in this lecture is insane

[@timbookatuncommonsense8778]

As Clear as his chalk markings made for his Diagrams. I really would of understood him if he hadn't of kept not really getting to the point!. And his accent was hard for me to understand. Also I don't know if there is other lectures that goes with this one but I felt his class knew what he meant, allowing them to complete the process of understanding what he is teaching them!!?🤗🤔🧐 No Doubting the Lecturers Intelligence!. And I could probably get it!;if I watched this lecture a couple more Times!!😄🤓🤡🤑🤯🤫🤔🤫

[@rababmaroc3354]

great job thank you for sharing Mr.

[@kingkactus]

I love this video. Interesting discussion on finding a way to determine volatility between assets with the same returns

[@sahavaschalermchaiwat624]

Thank you so much MIT. I have learn so much from this great stuff!

[@mikemian]

Jake is wrong in a few regards: 1) Cash has a zero to negative return based how much money the reserve bank prints each year or the CPI. Historically cash has devalued about 7% a year based on M2, or conservatively, at least the CPI. Cash, by definition cannot have a positive return. 2) A lotteries expected return is based on the current jackpot sometime jackpots get high enough that they become value for money bets - so the return and standard deviation would be higher than 1 (100%). 3) Analysis has shown that only the best VCs (top 25%) do better than ETFs, and that most VCs actually perform worse than the stock market. ETFs as a whole should perform almost exactly the same as stocks, though sectors may under/over perform the general market. 4) The return on real estate has historically been lower than stocks.

[@KB-ke3fi]

whoa....an actual chalkboard? Love it. The chalk hitting the board at 8 am always kept waking me up.

[@nicolaschen5809]

Good bless the free content avalaible in this times.

[@Mark-bc9ib]

Grateful for this. Thank you for uploading.

[@greggjaclin4810]

Great lecture and interesting topics. Thanks for sharing.

[@melissaharvey7177]

Do you have a managed portfolio?

[@lbevanlb]

absolutely incredible lecture.

[@chTomokz]

I am enjoy watching from Tokyo, Japan. and am a 52years lady. Thank you for giving a great lecture!

[@AlphaKingofGlory]

The calculation benefit is in identifying the best possible solution which in turn reduces the effort necessary to overcome the negative. 28:13

[@cjasgill1]

I feel a lot smarter after watching this

[@Victor_976]

This is great stuff

[@supaclass760]

Love these MIT courses!

[@alexkess8506]

Thank you MIT and Professor Xia!

[@vtss1336]

I don't know how i came here & im not even interested in this but im watching & learning what he is lecturing. Damn....

[@hanhangao6541]

he is incredible

[@StephenDoty84]

Really? I found him "credible." ;)

[@SolisDaName]

Do you work for the CCP?

[@shashanksrivastav4353]

Thank you MIT for this learning lecture.

[@kimyoung8414]

Jake, you are wonderful

[@kiran10110]

He seems like a great prof :) Rare to see profs that really try to listen to their students. These were always my favourite profs in school.

[@ashleynoelle7429]

“I’m gonna write down everything and take my time”- that’s a good mentor.

[@lordofwrongs]

yeah bebe. u got it.

[@phebeovercomer8851]

Thank You so much for these valuable financial education and its free for all! My gratitude!!!

[@AlpacaCheese]

Good lecture where I can understand and follow along, good stuff

[@nabilwalid9774]

I wish my Professors approach their lectures like this. Trying their best to simplify the concepts of a new topic. All my professor does is follow the textbook lol

[@PG-ms5rh]

thats cause he is a lazy Piece of Shit

[@franciscoreyes7370]

Probably because their course coordinators and department chairs make them cover specific topics from the book. In upper division courses, professors tend to have more flexibility.

[@ryansmith5459]

"The tendency is to stay with the crowd -- for survival..." Exactly.

[@olyo167]

good info you do not ramble on and repeat the same thing over and over. thank you!

[@notezekiel]

This is the best video I’ve ever seen.

[@izayasanderson3471]

wow, that's all I gotta say, this is incredible

[@trippasnippa119]

I feel like i just had the craziest realization. Kids cant learn shit in schools in america pre college is cause teachers have a quota they have to meet and they pre write things on the board and rush through slides and the kids dont have a chance to understand anything thoroughly its just a memory game. This guy gets it about taking his time and writing through everything. I like him.

[@edrian3485]

every industry have their own agenda, there is conflict of interest. best way to survive & thrive in the financial markets is build your own infrastructure.. but that just one part of human needs to fullfil freedom (act) and free will (thoughts) there's more human needs like psychological etc.. thats is the optimised version of life which bring clarity and value

[@hebbez300]

@@edrian3485 plagiarism

[@TheTennisMachine]

Great course that should be learned by all students in school

[@ryanr8866]

whoever called out google and apple stock, mad respect bro hope u living lavish if u held

[@michaelramirez8245]

📈🚀🚀I find myself paying more attention to this video than my actual classes

[@davidr2421]

It's a real conundrum. Lectures you find online from MIT, Stanford, Harvord, etc, are so much better than the usual lecture you'd find at your own college. It's hard to even show up and listen. And in the end, why should you? Really goes to show that large components of the university system are obsolete.

[@benriggan5267]

really helpful information and insights, thanks for sharing!

[@BiscuitZombies]

Brilliant professor

[@yandhi4202]

gentleman at 1:26:00 was really interesting to hear from, glad he was included in the video

[@christhophergeorgelatorewa4275]

Due to the inflation cash has a negative return. Thank you FED and EZB!

[@SerDag330]

Simply perfect. Respect🙏🏻

[@kushpatel3446]

Amazing video, very well explained!!!

[@bilal7561]

20:01 Timestamp for me - I really want to watch the whole lecture, but it’s 2am, so I might fall asleep any second. Just ignore me, thanks.

[@manhoosnick]

Wakeup man

[@1inchlegendaka.icebrrg156]

YAAASSS QUEEEEENNN!!!

[@SleekMouse]

Next time just text or email yourself a link with the start time. This is asinine way of saving your place. Its been 3 weeks. Either you finished the lecture or you didn't, time to remove this personal use time stamp.

[@lavanyachauhan3222]

@@manhoosnick wow

[@sora_is_my_dad420]

who tf watches... at 2 am... nvm u do u boo, get that $

[@kevinchou1577]

He looks like the banker in Dark Knight

[@taffydjsr]

He's good with calculation

[@hanzz9083]

or an IRS meeting with joker

[@utkarsh12]

batman will find him and make him squeal

[@kevinchou1577]

He moved all of his student’s exam paper to a single safe location. Only he can know where it is.

[@ethancroft2560]

I was literally just thinking the same thing.

[@greatbear7153]

Totally valuable information

[@DrewShah]

This lecture was great

[@stevenguyen7479]

This instructor is amazing, Thx MIT.

[@veeecos]

For people wondering why variance and mean of coin flip is one. Let us assume a fair coin. P(Heads) = P(Tails) = 0.5. Assume you get +1 if you land heads and -1 if you land tails. Mean = 1*0.5 + (-1) * 0.5 =0. Variance = E(X- mean)^2. Variance = E(X^2) as mean is zero. E(X^2) = 1*1*0.5 + (-1)(-1)*0.5 = 1. Hence standard deviation is also 1.

[@blessed4success683]

Correct delivery 👏

[@collinsmuga3408]

Thank you so much for the insight. what a break though.

[@chrisxcollazo]

Great video! I really learned so much 🤑🙌

[@xwclsg]

What a great teacher! He can explain things very well.

[@unnamedsoldier88]

In one word, diversify your portfolio to maximize your returns. Thanks for the video.

[@randomz8065]

not really lol, only if markets were that easy wouldn't that be wonderful

[@bobgorn2550]

Yes and No, more Like: to lower your risk

[@faisalamin_369]

best class ever

[@humbertochavez6572]

Professor XIA’s lecture is brilliant and an eye-opener for my lil itsy bitsy tiny brain

[@munchies9]

Damn, those good old days of a drawing board, today is everything on teams HAHAHAH