Leveraging CAPM and MPT for Strategic Financial Management at Alejos Capital Group
At Alejos Capital Group, we use advanced financial models to make informed decisions and maximize returns. Here’s how we use the Capital Asset Pricing Model (CAPM) and Modern Portfolio Theory (MPT) to manage and grow our investments, explained for both novice and experienced investors.
Capital Asset Pricing Model (CAPM)
What is CAPM?
CAPM helps determine the expected return on an investment by considering its risk. This model is essential for making investment decisions that align with our goals.
Formula:
$$\text{Expected Return} = R_f + \beta (R_m - R_f)$$
Where:
- R_f = Risk-free rate (e.g., U.S. Treasury bonds)
- \(\beta\) = Beta (a measure of an investment’s volatility compared to the market)
- R_m = Expected market return
Example Projects
We evaluated three potential projects:
- Project Alpha: Buying a doctor’s practice that is already generating revenue.
- Project Beta: Investing in residential rental properties.
- Project Gamma: Holding stocks with options in a vertical spread structure.
Assumptions
- Risk-free rate (\( R_f \)): 4.803%
- Market return (\( R_m \)): 13.13%
Expected Returns
Project Alpha: Buying a Doctor’s Practice
- Expected Annual Cash Flow: $400,000
- Beta: 1.2
- Impact in Year 3: 6 months of cash flow lost ($200,000 reduction)
Expected Return Calculation:
$$\text{Expected Return}_\text{Alpha} = 4.803\% + 1.2 \times (13.13\% - 4.803\%)$$
$$\text{Expected Return}_\text{Alpha} = 14.7954\%$$
Net Present Value (NPV) Calculation over 5 years:
$$\text{NPV}_\text{Alpha} = \sum_{t=1}^{5} \frac{400,000}{(1 + 0.147954)^t}$$
Adjusted for Year 3 impact:
$$\text{NPV}_\text{Alpha} = \frac{400,000}{(1 + 0.147954)^1} + \frac{400,000}{(1 + 0.147954)^2} + \frac{200,000}{(1 + 0.147954)^3} + \frac{400,000}{(1 + 0.147954)^4} + \frac{400,000}{(1 + 0.147954)^5}$$
$$\text{NPV}_\text{Alpha} \approx \$1,220,612$$
Project Beta: Residential Rental Properties
- Expected Annual Cash Flow: $300,000
- Beta: 0.8
- Impact in Year 3: 6 months of cash flow lost ($150,000 reduction)
Expected Return Calculation:
$$\text{Expected Return}_\text{Beta} = 4.803\% + 0.8 \times (13.13\% - 4.803\%)$$
$$\text{Expected Return}_\text{Beta} = 11.4646\%$$
Net Present Value (NPV) Calculation over 5 years:
$$\text{NPV}_\text{Beta} = \sum_{t=1}^{5} \frac{300,000}{(1 + 0.114646)^t}$$
Adjusted for Year 3 impact:
$$\text{NPV}_\text{Beta} = \frac{300,000}{(1 + 0.114646)^1} + \frac{300,000}{(1 + 0.114646)^2} + \frac{150,000}{(1 + 0.114646)^3} + \frac{300,000}{(1 + 0.114646)^4} + \frac{300,000}{(1 + 0.114646)^5}$$
$$\text{NPV}_\text{Beta} \approx \$1,029,475$$
Project Gamma: Holding Stocks with Options in a Vertical Spread Structure
- Expected Annual Cash Flow: $250,000
- Beta: 1.5
- Options Value in Year 3: $150,000 (exercise value of options)
Expected Return Calculation:
$$\text{Expected Return}_\text{Gamma} = 4.803\% + 1.5 \times (13.13\% - 4.803\%)$$
$$\text{Expected Return}_\text{Gamma} = 17.2935\%$$
Net Present Value (NPV) Calculation over 5 years:
$$\text{NPV}_\text{Gamma} = \sum_{t=1}^{5} \frac{250,000}{(1 + 0.172935)^t} + \frac{150,000}{(1 + 0.172935)^3}$$
$$\text{NPV}_\text{Gamma} \approx \$886,279$$
Summary of NPVs
| Project | Description | NPV |
|---|---|---|
| Project Alpha | Buying a Doctor’s Practice | $1,220,612 |
| Project Beta | Residential Rental Properties | $1,029,475 |
| Project Gamma | Stocks with Options | $886,279 |
Applying Modern Portfolio Theory (MPT)
Why MPT?
MPT helps us balance risk and return by diversifying investments. This ensures a more stable and profitable portfolio.
Risk Assessment:
| Project | Risk Level | Description |
|---|---|---|
| Project Alpha | Moderate | Stable returns |
| Project Beta | Low | Consistent rental income |
| Project Gamma | High | Significant returns through options |
So What?
By combining these projects, we can create a diversified portfolio that maximizes returns while managing risk. This strategic approach ensures long-term financial growth and stability for Alejos Capital Group.
Portfolio Average Return
Using MPT and CAPM, we calculated the portfolio's average return based on equal investment in each project.
Expected Returns:
| Project | Expected Return |
|---|---|
| Project Alpha | 14.7954% |
| Project Beta | 11.4646% |
| Project Gamma | 17.2935% |
Weighted Average Return Calculation:
$$\text{Portfolio Return} = \left(\frac{1}{3} \times 14.7954\%\right) + \left(\frac{1}{3} \times 11.4646\%\right) + \left(\frac{1}{3} \times 17.2935\%\right)$$
$$\text{Portfolio Return} \approx 14.52\%$$
Visual Representation of Data
Expected Returns:
| Project | Expected Return |
|---|---|
| Project Alpha | 14.7954% |
| Project Beta | 11.4646% |
| Project Gamma | 17.2935% |
NPV Calculation Terms:
| Project | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Sum |
|---|---|---|---|---|---|---|
| Alpha | 348,260 | 303,187 | 143,455 | 227,554 | 198,156 | 1,220,612 |
| Beta | 269,250 | 241,589 | 106,913 | 217,023 | 194,700 | 1,029,475 |
| Gamma | 213,190 | 181,619 | 247,440 | 131,788 | 112,242 | 886,279 |
This structured approach ensures that our investment strategies are both accessible and effective for all stakeholders, providing clear insights into how we manage and grow our investments at Alejos Capital Group.
Signing Off,
Erik A.