Portfolio Optimization: An In-Depth Beginner’s Guide
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What’s common between Blackrock, Vanguard, and State Street?
They all have launched portfolio optimization tools to satisfy the needs of intermediate and experienced investors.
However, these tools don’t fascinate rookie investors, who like to keep all their eggs in one basket and have secured a few returns—overestimating their capability.
For investors with experience, portfolio optimization is the key to survival.
In this article, we’re targeting you, the rookie investor, to learn and understand the importance and process of portfolio optimization before you lose your savings on a single investment.
Moreover, if you’ve run out of beginners’ luck and have started to see the downside of filling your portfolio with only the high-risk-reward stock options, please read on.
What Is Portfolio Optimization?
Portfolio optimization goes beyond the stock market and reaches any investment opportunity that involves assets. The basic objective of portfolio optimization is to minimize your risk and maximize your returns.
However, it doesn’t express the maximum returns offered by an asset. It maximizes the potential returns to your risk tolerance. If you have a higher risk tolerance, your portfolio could generate better returns (or losses).
How Does Portfolio Optimization Work?
A few variable steps are involved in the expression of portfolio optimization.
Depending on the type of PO models and the investment objectives, the optimization process should change.
In brief, here are the steps involved in portfolio optimization:
Defining investment objectives
Gathering technical data
Establishing risk and return measures such as expected return, Sharpe ratio, standard deviation, etc.
Define constraints such as sector exposure, asset allocation, etc.
Select an optimization model
Optimization of portfolio
Monitoring and maintenance
Let’s analyze two hypothetical stocks A and B with the Sharpe ratio. We’re considering the Sharpe ratio to inject risk into the equation.
Stock A Returns:
Year 1: 10%
Year 2: 15%
Year 3: 5%
Stock B Returns:
Year 1: 5%
Year 2: 8%
Year 3: 12%
Mean Return of Stock A = (10% + 15% + 5%) / 3 = 10%
Mean Return of Stock B = (5% + 8% + 12%) / 3 = 8.33%
Standard deviation for Stock A = sqrt[(10-10)^2 + (15 - 10)^2 + (5 - 10)^2)] / sqrt(3) = 4.08%
Standard Deviation of Stock B = sqrt[(5 - 8.33)^2 + (8 - 8.33)^2 + (12 - 8.33)^2)] / sqrt(3) = 2.93%
Now, let’s assume the Risk-Free Rate at that moment is 3%.
The Risk-Free Rate is the hypothetical return on investment with zero risk. Typically, government-issued small-term bonds such as Treasury bonds or Treasury bills are indicative of it.
Risk-Free Rate acts as a baseline for evaluating the expected return of other investments.
Now, depending on your risk tolerance and expected returns, we set Target Sharpe Ratio at 0.8. A higher Sharpe Ratio refers to a greater return for a specific level of risk.
We’ll now prepare a table assigning weights on both Stock A and B considering increments of 10%.
For Stock A, we’ll start from 0%, 10%, 20%...80%, 90%, 100%.
For Stock B, we’ll assign the weight as 100%, 90%, 80%...20%, 10%, 0%.
However, we may not include them all to shorten the calculations.
Before we do that, let’s devote a few moments to the Sharpe Ratio formula.
Sharpe Ratio: (Portfolio Expected Return - Risk-Free Rate) / Portfolio Standard Deviation
If the weight of Stock A and B are 60% and 40% respectively, then Portfolio Expected Return would be = (0.60 * 10%) + (0.40 * 8.33%) = 9.5% For each additional investment, keep adding to the equation.
For Portfolio Standard Deviation, the calculation would be = sqrt[(0.60^2 * 4.08%^2) + (0.40^2 * 2.93%^2) + (2 * 0.60 * 0.40 * 4.08% * 2.93% * 0.6)] = 3.18%
Similarly, keep adding to the equation for each additional opportunity.
Generic formula for Portfolio Expected Return = w1 * R1 + w2 * R2 + ... + wN * RN
Where:
w1, w2, ..., wN are the weights of the assets in the portfolio (sum of weights should be 1)
R1, R2, ..., RN are the expected returns of the assets
Generic formula for Portfolio Standard Deviation = sqrt(w1^2 * σ1^2 + w2^2 * σ2^2 + ... + wN^2 * σN^2 + 2 * w1 * w2 * ρ12 * σ1 * σ2 + ... + 2 * w1 * wN * ρ1N * σ1 * σN + ... + 2 * wN-1 * wN * ρ(N-1)N * σ(N-1) * σN)
where:
σ1, σ2, ..., σN are the standard deviations of the assets
ρ12, ρ1N, ..., ρ(N-1)N are the correlation coefficients between the assets
Without further ado, let’s find the optimal allocation:
In this example, the closest optimization combination belongs to 80% Stock A weight and 20% Stock B weight.
However, in real situations, many different factors may influence the optimization score and your preference. One of them is asset classes, which are also discussed later in this article.
Although we’ve used Sharpe Ratio for the calculation, it’s not an optimization technique and is commonly used as a tool in the context of mean-variance optimization. Additionally, Efficient Frontier curves generated through Excel are used for portfolio optimization.
Asset Classes in Portfolio Optimization
In investment, asset classes are categories that share similar characteristics and behavior. Typically, an investor includes different asset classes in their portfolio to diversify risks and enhance returns.
Equities/Stocks
Equities and stocks represent ownership in publicly traded companies. These types of investments entitle you to the profit share and dividends derived from the said company. Equities and stocks are considered more risky and volatile than other asset classes.
Fixed Income/Bonds
To balance the risky characteristics of publicly traded stocks, government bonds, treasury bills, and corporate bonds are included in portfolios that offer stability and fixed return to investors.
Cash and Cash Equivalents
Cash and cash equivalents include money market funds, certificates of deposit (CDs), and short-term Treasury bills. These assets offer liquidity and stability, acting as a buffer against market volatility.
Real Estate
Real estate investments include residential, commercial, and industrial properties, as well as real estate investment trusts (REITs). Real estate offers potential income through rental yields and the potential for capital appreciation.
Commodities
Physical goods like gold, oil, natural gas, agricultural products, and metals are considered commodities. This type of asset class provides diversification benefits and can act as a hedge against inflation.
The Bottom Line
As an investor, it’s important to realize the importance of balance and stability in your portfolio. Through this article, we’ve tried to introduce you to the fascinating and a bit overwhelming calculations of portfolio optimization. You’ll, hopefully, benefit from the discussion and start using analytical tools before following your raw instincts.