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Fund managers build portfolios, should you?
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doctorpot1 joined discussion · Nov 20, 2022 12:51

Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio

TLDR: Many Youtubers and even Warren Buffett had been asking us to just buy $SPDR S&P 500 ETF(SPY.US)$, but according to the Modern Portfolio Theory (MPT), this isn't the most optimal. By adding 13.63% of $Invesco QQQ Trust(QQQ.US)$ and 43.22% of $SPDR Gold ETF(GLD.US)$ to the mix, you could get the same returns of 9.63% but with risk lowered by about 3%. Or if you want the same level of risk but a higher reward, it suggest that you ignore S&P500 and for just go for 79.05% $Invesco QQQ Trust(QQQ.US)$ and 20.95% $SPDR Gold ETF(GLD.US)$ to get a whooping 12.37% returns for the same risk.
However, the most optimal risk reward ratio portfolio as suggested by MPT is to put 59.85% into $Invesco QQQ Trust(QQQ.US)$ and 40.15% into $SPDR Gold ETF(GLD.US)$ which should have a 11.41% return with a risk of 13.24%. This is a higher reward and lower risk portfolio as compared to the base case. Wait? What? How? Read more to find out There is a simple tool included in the post that can help you apply MPT with ease.
Story time
Modern Portfolio Theory (MPT), as pioneered by Nobel Prize winner Harry Markowitz, is a mathematical framework to help investors maximise return and minimise risk. To put it in super simplified terms it is just
1. Taking all your stocks that you hold, calculate risk reward ratio for every single possible permutation of allocation and find the best ones (i.e. check risk reward if you have 100% stock A, 0% stock B, then check risk reward if you have 99% stock A, 1% stock B, and so on).
2. Check if adding another asset could help improve the risk return ratio or not.
What do I need to know first?
To understand MPT we first need to understand 3 concepts first.
1. Expected Return
2. Variance
3. Correlation
Expected Returns: Expected Return is just what is the likely return if we take into consideration all cases, and in a mathematical form it is just simply multiplying the probability of each scenario by the outcome amount, then adding them all up.
So for example, if there is this fair 2-sided coin flip game where you will win $1 if the coin lands on heads, and lose $1 if the coin lands on tail. You know that the probability of landing on heads or tails is 50% (1/2). so that means the chance of winning $1 is 50%, and so is the chance of losing $1.
If we were to calculate the expected returns it will be, just multiplying the chance with the outcome, then adding them up. I.e. We have 50% chance of winning $1, so we would multiply $1 by 50%, which gives us an expected sub-returns $0.50 for this scenario. Then since we also have a chance of losing $1, so we would multiply-$1 by 50%, which gives us an expected sub-returns -$0.50 in this scenario. Adding them up, the expected return for the game is $0 (+$0.5-$0.5).
Variance: Variance is just the measure of how far the numbers can deviate from the average number (mean).
For example if there is a stock with a average price of $100, but it go as low as $50 and as high as $150. This stock have a much higher variance as compared to a stock with a average price of $100, but it go as low as $99 and as high as $101.
Correlation: Correlation is just a measure of how similar or different 2 things moves together. It can be positively correlated which means the 2 things moves together in the same direction. It can be negatively correlated which when one goes up, the other goes down. It can also have no correlation, which mean there is like no link. This is a number between -1 and 1.
For example, $S&P 500 Index(.SPX.US)$ and $Dow Jones Industrial Average(.DJI.US)$ are highly positively correlated as they tend to move up and down together as you can see in the chart below.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
How does it help us to optimise risk and reward?
MPT used standard deviation (a function of variance) in the stock price as a measure of risk. Therefore, $Tesla(TSLA.US)$ which have a higher variance will be seen as riskier as compared to $Coca-Cola(KO.US)$. Which kind of make sense as if you are unlucky and bought at the highest price of both companies and then it crashes down back to the mean, it is more painful for Tesla as compared to Coca Cola.
Because MPT uses standard deviation as a measure for risk, therefore it also suggests that we look for stocks that have negative correlation to our portfolio to help us reduce our risk. This is because doing so will lower help to reduce the standard deviation of our portfolio. Which make sense because if we have 2 stocks that moves up and down together, we will see our portfolio fly and crash way faster as compared to having 2 stocks that moves up when the other move down.
A key tool in MPT that helps us optimise our risk and reward of our portfolio is known as the efficient frontier, where it plots the expected return against the risk (standard deviation) of our portfolio, using historical data. We are suppose to plot the risk and reward of all the permutation of allocation available in our portfolio (i.e. 100% of stock A & 0% of stock B, 99% of stock A & 1% of stock B, 98% of stock A & 2% of stock B, and so on) on the graph to find the best possible allocations. It will end up looking something like the chart below where the best possible allocation are on the blue curve.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
Any point on the curve is the best return you can get for any given risk you want to take, and there will be 1 point that is the most optimal. However, that is a lot of data to process, tons of math and statistics to be done. Ain't nobody got time for that.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
How can retail investors like us use MPT?
It is tedious for us to calculate the efficient frontier, but computers are very good at processing tons of data, and do math and statistics for us. Therefore, we could use online tools for that, and I found one free online tool (https://www.portfoliovisualizer.com/efficient-frontier) for it. So I'm using it to apply MPT on the good old saying by $Berkshire Hathaway-A(BRK.A.US)$'s Warren Buffett, which is for us retail investors to just DCA on $SPDR S&P 500 ETF(SPY.US)$.
To make things simple, I just picked out $SPDR S&P 500 ETF(SPY.US)$, $Invesco QQQ Trust(QQQ.US)$ and $SPDR Gold ETF(GLD.US)$ to test it out.
Why QQQ? because we are in the high tech era and QQQ tracks $Nasdaq Composite Index(.IXIC.US)$ which have all the best high tech stocks in them.
Why GLD? because this is an ETF for gold and many people are saying every portfolio should have a bit of gold in them.
Why no STI or S-REITS? because this free tool don't have $FTSE Singapore Straits Time Index(.STI.SG)$ or $CSOP iEdge SREIT ETF US(SRU.SG)$ available
From the tool we can see the expected return and risk of each of the stocks, as well as the correlation between them. SPY and QQQ are highly correlated which means their price tends to move in the same direction. Where as Gold (GLD) have no correlation with either of them, which means gold price moves on its own and is not affected by the movement of SPY and QQQ.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
For the time period, I had choosen 2005 to 2022. The app will then take the performance of each of the 3 stocks and determine automatically their risk reward profile based on that time period. They only had data from 2005 so I can't choose any earlier As the base case, I allocated 100% to SPY and none to QQQ and GLD. This will allow us to visualise how good or bad this 100% SPY portfolio is compared to the best possible portfolio.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
As we can see the result of the efficient frontier, going 100% SPY is not the best option available. We could have increased our return by 2.74% for the same amount of risk taken, or we could have reduce our risk by 3.24% for the same amount of returns. Or both increase our return by 1.78% while reducing our risk by 1.91%.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
From the historical data, having 100% in SPY have an expected return rate of 9.63% and a risk of 15.15%. However, we could be getting an expected return of 12.37% for the same amount of risk, by choosing to hold 79.05% in QQQ and 20.95% in GoLD instead.
However, if we are risk adverse and would like a lower risk for the same 9.63% return, we can allocate 43.15% to SPY and add in 13.63% into QQQ and 43.22% into GoLD. On top of that, the efficient frontier also tells us the most optimal portfolio, with the best risk reward ratio too. It is the portfolio with the highest Sharpe ratio which allocates 59.85% to QQQ and 40.15% into GoLD.
What if we want to time the market can MPT help?
Of course we can! Do you still remember that MPT uses historical data to compute the risk reward ratio. So by adjusting the time period we could be able to optimise the portfolio further. For example, if we think that the current market is the same as the period after the 2008 financial, then we can shift the start date to be 2009 to calculate the risk reward based on that period.
Explained Simply: Modern Portfolio Theory, Optimising Risk and Reward of your portfolio
What is interesting is that 100% SPY is still not the best portfolio ever. This is probably because QQQ has the highest reward potential among the 3 stocks.
Since many stocks have crashed real bad, such as $Palantir(PLTR.US)$, $Warner Bros Discovery(WBD.US)$, $Alibaba(BABA.US)$, $NIO Inc(NIO.US)$, $Invesco China Technology ETF(CQQQ.US)$, $Futu Holdings Ltd(FUTU.US)$. We could also try and add them to see how it goes
Conclusion: Testing it out
What is knowledge without testing them out right? So to conclude, let us use a Moo Moo's feature known as paperfolio to test MPT out. Using paperfolio, we can build portfolio and track their performance over time. Therefore, I will be leveraging on them to test out if MPT works over the long term. Maybe we can do an annual review on the portfolio.
Here are the 4 portfolio, do follow so that we can track them together
Disclaimer: Community is offered by Moomoo Technologies Inc. and is for educational purposes only. Read more
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doctorpot1
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crawled out of poverty, working towards FIRE!! (financial independence, retired early)
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