My learnings from Modern Portfolio Theory...
I've been trying to learn key quant topics in my free time. So I was reading on Modern Portfolio Theory and this plot was generated using Monte Carlo Simulations.
At its core, MPT suggests that investors can construct an "optimal" portfolio by considering the trade-off between risk and return. The key ideas illustrated in this graph are:
1. Diversification: By combining assets with different risk-return profiles, investors can create portfolios that offer better risk-adjusted returns than any individual asset.
2. Efficient Frontier: This is the set of optimal portfolios that offer the highest expected return for a defined level of risk, or the lowest risk for a given level of expected return.
3. Sharpe Ratio: A measure of risk-adjusted performance, calculated as (return - risk-free rate) / volatility. Higher is better.
Each blue dot represents a possible portfolio allocation.
1. The x-axis shows volatility (risk), while the y-axis shows expected return.
2. The color gradient from light to dark blue indicates increasing Sharpe ratios.
3. The red dashed line is the Efficient Frontier.
4. The red star marks the Maximum Sharpe Ratio portfolio.
5. The green star indicates the Minimum Volatility portfolio
**Interpretation**
1. The "cloud" of dots shows all possible portfolios. Its shape (often called the Markowitz Bullet) illustrates how diversification can improve the risk-return profile.
2. Portfolios on the upper edge of this cloud (the Efficient Frontier) are considered optimal - you can't get higher returns without taking on more risk.
3. The Maximum Sharpe Ratio portfolio (red star) offers the best risk-adjusted return.
4. The Minimum Volatility portfolio (green star) is the least risky efficient portfolio.
5. Portfolios below the Efficient Frontier are suboptimal - you could achieve either higher returns for the same risk or lower risk for the same return.
In practice, investors would choose a portfolio along the Efficient Frontier based on their risk appetite.
More conservative investors might lean towards the green star, while those comfortable with more risk for potentially higher returns would move towards the red star or beyond.
At its core, MPT suggests that investors can construct an "optimal" portfolio by considering the trade-off between risk and return. The key ideas illustrated in this graph are:
1. Diversification: By combining assets with different risk-return profiles, investors can create portfolios that offer better risk-adjusted returns than any individual asset.
2. Efficient Frontier: This is the set of optimal portfolios that offer the highest expected return for a defined level of risk, or the lowest risk for a given level of expected return.
3. Sharpe Ratio: A measure of risk-adjusted performance, calculated as (return - risk-free rate) / volatility. Higher is better.
Each blue dot represents a possible portfolio allocation.
1. The x-axis shows volatility (risk), while the y-axis shows expected return.
2. The color gradient from light to dark blue indicates increasing Sharpe ratios.
3. The red dashed line is the Efficient Frontier.
4. The red star marks the Maximum Sharpe Ratio portfolio.
5. The green star indicates the Minimum Volatility portfolio
**Interpretation**
1. The "cloud" of dots shows all possible portfolios. Its shape (often called the Markowitz Bullet) illustrates how diversification can improve the risk-return profile.
2. Portfolios on the upper edge of this cloud (the Efficient Frontier) are considered optimal - you can't get higher returns without taking on more risk.
3. The Maximum Sharpe Ratio portfolio (red star) offers the best risk-adjusted return.
4. The Minimum Volatility portfolio (green star) is the least risky efficient portfolio.
5. Portfolios below the Efficient Frontier are suboptimal - you could achieve either higher returns for the same risk or lower risk for the same return.
In practice, investors would choose a portfolio along the Efficient Frontier based on their risk appetite.
More conservative investors might lean towards the green star, while those comfortable with more risk for potentially higher returns would move towards the red star or beyond.
Why is volatility considered as a measure of risk ?
What is expected return ? Won't everyone expect gangbuster returns, how is it even measured ?
1. Volatility is calculated as the standard deviation of returns. The calculation uses the covariance matrix of asset returns, which captures how the returns of different assets move together. .
The resulting standard deviation is then annualized by multiplying by the square root of 252. Why? because assuming 252 trading days in a year.
Higher volatility means larger price swings, which represents greater uncertainty about future returns.
More volatile assets have a higher chance of significant short-term losses, even if their long-term expected return is positive.
2. Expected returns is Mean of Historical Returns.
This method assumes that historical patterns will continue.
See more comments
Jordon Taye
Stealth
9 days ago
Interesting. For the first time, I am hearing about this, so not much idea on this. Quick questions:
1. What were the sources and datasets that you used for conducting this approach ?
2. What were the features you considered while generating the final dataset?
3. Also, if you share your approach on the pre-processing to make it to final dataset before getting this graph?
Blair Olive
Student
9 days ago
This is SOOOO SATISFYING thank you, this analysis is what I live and breathe to do.
Kendall Nadeen
Stealth
9 days ago
Pikachu with a heavy thunderbolt attack!!
Kendall Carmden
Stealth
9 days ago
MPT is an elegant explanation in theory but doesn't work when put to use in the markets. It's among the many things folks with finance degrees learn to unlearn if they work in the markets. I remember reading an article whee even Markowitz confessed to not using his theory lol. Will share the link if I find it
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