✏️ CAL Examples
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or
or
= (.12 * .50) + (.04 * .50) = 8%
E(r_C) = r_F + Sσ_C = 2% + .8 * 15% = 14%
Notation
= Return of Risk Free Assets
= Return of Portfolio of Risky Assets
= Return of Complete Portfolio
= Expected Return of Risky/Complete Portfolio
Occasionally I use as shorthand for
= % of Portfolio in Risky Assets
= % in Risk-Free Assets
= Standard Deviation
= Sharpe Ratio
Variance = Standard Deviation^2
Standard Deviation = SQRT of Variance
✏️ You manage the following risky portfolio:
A client walks in and says that they only want a . What percentage of their assets should be in the risky portfolio?
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- Equation → a. We want , so we need a formula with in it. We can’t use because we don’t know or . However, we can use because we know both risk levels.
- Plug 🔌 →
- Solve 🚂 →
- 🧠 → This client will invest 45% of their net worth in risk assets. ✅
✏️ You manage the following risky portfolio:
0.11107 | 0.07543 |
A client walks in and says that they only want a . What percentage of their assets should be in the risky portfolio?
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We approach this by finding an equation and plugging numbers into it, then solving for y. This approach is a key tool for solving questions like this. It is often called “Plug and Chug,” because all you have to do is plug numbers into an equation and chug through a little algebra until you get the answer. Click the “help” link below for details.
Plug and chug: (help)
- Equation:
- Plug:🔌
- Solve: 🚂
- Reflect: 🧠
This client will invest 198% of their net worth in risk assets.
To achieve these returns, the client would have to invest 198.107% of their assets in your portfolio. It is unlikely that they would be able to borrow this much money at anything near , so this target is likely unrealistic. You may have to guide them toward more realistic goals.
… However, if they could borrow of their assets at the risk free rate, and did so, their final expected return would be
✏️ Suppose that 50% of your complete portfolio is in risky assets and 50% of your risky assets are equities. What percent of your money is invested in equities?
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Half of your money is in risk assets and half of that is in equities, so you have in equities.
In general:
% of complete portfolio in equities = % in risk asset weight of equities in risk assets. ✅
✏️ Suppose that 80% of your complete portfolio is in risky assets and that 60% of your risky assets are equities. What percent of your money is invested in equities?
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60% of 80% ✅