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LM01 Portfolio Risk and Return: Part I 2025 Level I Notes © IFT. All rights reserved 1 LM01 Portfolio Risk and Return: Part I 1. Introduction ........................................................................................................................................................... 2 Investment Characteristics of Assets: Return (Prerequisite Material) .......................................... 2 Return ..................................................................................................................................................................... 2 Money-Weighted Return or IRR (Prerequisite material) ................................................................... 3 Time-Weighted Rate of Return (Prerequisite material) ..................................................................... 4 Annualized Return (Prerequisite material) ............................................................................................. 5 Other Major Return Measures (Prerequisite material) ....................................................................... 5 2. Historical Return and Risk ............................................................................................................................... 8 3. Other Investment Characteristics ................................................................................................................. 8 4. Risk Aversion and Portfolio Selection & The Concept of Risk Aversion ........................................ 9 The Concept of Risk Aversion ........................................................................................................................ 9 5. Utility Theory and Indifference Curves ....................................................................................................... 9 6. Application of Utility Theory to Portfolio Selection ............................................................................11 7. Portfolio Risk & Portfolio of Two Risky Assets .....................................................................................14 Portfolio of Two Risky Assets .....................................................................................................................14 8. Portfolio of Many Risky Assets ....................................................................................................................16 9. The Power of Diversification ........................................................................................................................16 10. Efficient Frontier: Investment Opportunity Set & Minimum Variance Portfolios ................16 Investment Opportunity Set ........................................................................................................................16 Minimum Variance Portfolios .....................................................................................................................17 11. Efficient Frontier: A Risk-Free Asset and Many Risky Assets .......................................................17 12. Efficient Frontier: Optimal Investor Portfolio ....................................................................................18 Summary ...................................................................................................................................................................20 Required disclaimer: IFT is a CFA Institute Prep Provider. Only CFA Institute Prep Providers are permitted to make use of CFA Institute copyrighted materials which are the building blocks of the exam. We are also required to create / use updated materials every year and this is validated by CFA Institute. Our products and services substantially cover the relevant curriculum and exam and this is validated by CFA Institute. In our advertising, any statement about the numbers of questions in our products and services relates to unique, original, proprietary questions. CFA Institute Prep Providers are forbidden from including CFA Institute official mock exam questions or any questions other than the end of reading questions within their products and services. CFA Institute does not endorse, promote, review or warrant the accuracy or quality of the product and services offered by IFT. CFA Institute®, CFA® and “Chartered Financial Analyst®” are trademarks owned by CFA Institute. © Copyright CFA Institute Version 1.0
LM01 Portfolio Risk and Return: Part I 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This reading covers:  Investment characteristics of assets in terms of their return and risk.  How to determine what assets are appropriate for a portfolio.  How to construct an indifference curve and use it in the selection of an optimal portfolio using two risky assets.  How to construct an optimal risky portfolio. Investment Characteristics of Assets: Return (Prerequisite Material) Return Return can come in two forms:  Periodic income through interest payments or dividends.  Capital gains when the price of the asset you hold increases. We now look at the various types of return measures and their applicability. Holding Period Return Holding period return is the return earned on an asset during the period it was held. It is calculated as a sum of capital gain (price appreciation) and periodic income. HPR = PT − P0 + IT P0 where: PT - P0 = capital gain component IT = Income earned during period T PT = price at the end of the period P0 = price at the beginning of the period Arithmetic or Mean Return Arithmetic return is a simple arithmetic average of returns. Assume you have three stocks A, B, and C with returns of 10%, 20%, and 30% respectively. The collective return from the three stocks is (10 + 20 + 30)/3 = 20%. Geometric Mean Return Geometric mean return is the compounded rate of return earned on an investment. Geometric mean return = [(1 + Ri1) ∗ (1 + Ri2) ∗ ... . .∗ (1 + RiT)] 1 T − 1 Assume you have a stock A which returns 10%, 20%, and 30% in years 1, 2, and 3 respectively. What is the mean return earned? Geometric mean return = [(1.1) (1.2) (1.3)]0.333 – 1 = 19.7%
LM01 Portfolio Risk and Return: Part I 2025 Level I Notes © IFT. All rights reserved 3 Money-Weighted Return or IRR (Prerequisite material) Money-weighted return is the internal rate of return on money invested that considers the cash inflows and cash outflows, and calculates the return on actual investment. Money-weighted return is a useful performance measure when the investment manager is responsible for the timing of cash flows. This is often the case for private equity fund managers. Example Given the data below, compute the holding period return, arithmetic mean return, geometric mean return, and money-weighted return. Assume no withdrawals except at the end of year 3. Year Assets under management at start of year (millions of $) Net return 1 30 10% 2 33 -5% 3 35 15% Solution: Holding period return: Holding period = 3 years Return = 1.1 x 0.95 x 1.15 = 1.20175 = 20.175% Arithmetic mean: Return = (10 – 5 + 15)/3 = 6.67% Geometric mean: Return = (1.1 x 0.95 x 1.15) 1 3⁄ − 1 = 6.317% Money-weighted return: To calculate the money-weighted return, we must know the net cash flows (cash inflows and outflows) for every year. So, let us draw a table and fill in the values and derive some others to get the values for CF0, CF1, CF2, and CF3. Year 1 Year 2 Year 3 Balance from previous year 0 33.00 31.35 New investment by investor 30.00 0 3.65 Withdrawal by investor 0 0 0 Net balance at start of year 30.00 33.00 35.00 Investment return for year 10% -5% 15% Investment gain (loss) 3.00 (1.65) 5.25 Balance at end of year 33.00 31.35 40.25 Now that we have the cash flows for the three years, let’s use the financial calculator to
LM01 Portfolio Risk and Return: Part I 2025 Level I Notes © IFT. All rights reserved 4 calculate IRR. CF0 = -30; CF1 = 0; CF2 = -3.65; CF3 = +40.25 IRR = 6.62% Time-Weighted Rate of Return (Prerequisite material) The time-weighted rate of return measures the compound growth rate of $1 initially invested in the portfolio over a stated measurement period. The time-weighted return can be calculated using the following steps: 1. Break the overall evaluation period into sub-periods based on the dates of cash inflows and outflows. 2. Calculate the holding period return on the portfolio for each sub-period. 3. Link or compound holding period returns to obtain an annual rate of return for the year (the time-weighted rate of return for the year). 4. If the investment is for more than a year, take the geometric mean of the annual returns to obtain the time-weighted rate of return over that measurement period. Consider the following example: Time Outflow Inflow 0 $20.00 to purchase the first share 1 $22.50 to purchase the second share $0.50 dividend received on first share $1.00 dividends ($0.50 x 2 shares); $47.00 from selling 2 shares @ $23.50 per share Calculating the TWRR for this example is relatively simple because cash flows only occur at the start/end of every year. We will follow the steps mentioned earlier: Steps 1: Break into evaluation period and value the portfolio at start/end of every period.  Value of the portfolio at the start of Year 1 (t = 0) is $20.00.  Value of portfolio at the end of Year 1 (t = 1) before the purchase of the new share is 22.50 + 0.50 = $23.00. Note that the dividend of $0.50 on the first share is received at the end of Year 1.  Value of the portfolio at the start of Year 2 (t = 1) after the purchase of the second share is 22.50 + 22.50 = $45.00. The dividend of $0.50 from the first share is paid out and is not considered as part of the portfolio.  Value of the portfolio at the end of Year 2 (t = 2) is 23.50 + 23.50 + 0.50 + 0.50 = $48.00. Both shares pay a dividend of $0.50 at the end of the second year. Step 2: Calculate the holding period return on the portfolio for each sub-period.  In this question the cash flows are taking place at the start/end of each period. Hence there are no sub-periods. Scenarios involving sub-periods will be covered in the next example. Step 3: Link or compound holding period returns to obtain an annual rate of return for the year.