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FIN 253

Fundamentals of Investment

TU BBS · Fourth Year · Four-year BBS curriculum

Requirement
elective
Full marks
100
Study Guide
11 units available

Chapter notes

Authoritative study guide across 11 syllabus units

Open a unit to read its study notes.

Unit 1: The Investment Environment· 8 LHs· ~6 marks

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The Philosophy and Scope of Investment

An investment is the current commitment of financial resources for a designated holding period with the expectation of deriving future monetary benefits that compensate the investor for the time value of money, expected inflation, and the uncertainty (risk) of future cash flows.

  • Real Assets versus Financial Assets:
    • Real Assets: Physical, tangible, or productive assets used to produce goods and services (land, commercial buildings, industrial machinery, technological patents). Real assets generate net wealth for an economy.
    • Financial Assets: Contractual claims against the cash flows generated by real assets (common stocks, corporate bonds, government treasury bills, bank deposits). Financial assets allocate existing wealth and productive output among economic participants.

The Two-Tiered Investment Decision Process

  1. Asset Allocation: The overarching decision regarding how to distribute an investor’s total wealth across broad asset classes (e.g., 60% domestic equities, 30% fixed-income sovereign bonds, 10% cash equivalents). Empirical research demonstrates that asset allocation accounts for more than 90% of long-term portfolio return variation.
  2. Security Selection: The granular decision of selecting specific individual securities within each asset class (e.g., choosing Himalayan Bank common shares within the equity allocation or 91-day T-bills within the cash allocation).
    • Top-Down Approach: Analyzes global and domestic macroeconomic conditions first, identifies thriving industrial sectors, and then picks superior individual stocks.
    • Bottom-Up Approach: Focuses directly on searching for undervalued individual stocks regardless of macroeconomic or sector forecasts.

Measuring Investment Returns

  1. Holding Period Return (HPR):
    HPR=Ending Price (P1)−Beginning Price (P0)+Cash Dividends / Interest (D1)P0\text{HPR} = \frac{\text{Ending Price } (P_1) - \text{Beginning Price } (P_0) + \text{Cash Dividends / Interest } (D_1)}{P_0}
    HPR=Capital Gains Yield+Dividend (Current) Yield=P1−P0P0+D1P0\text{HPR} = \text{Capital Gains Yield} + \text{Dividend (Current) Yield} = \frac{P_1 - P_0}{P_0} + \frac{D_1}{P_0}
  2. Annualized Holding Period Return (APR):
    Annualized HPR=(1+HPR)365n−1\text{Annualized HPR} = (1 + \text{HPR})^{\frac{365}{n}} - 1
    Where nn is the number of days the asset was held.
  3. Arithmetic Mean versus Geometric Mean Return:
    • Arithmetic Mean: Simple average; best predictor of expected return for a single upcoming period:
      Rˉarith=∑RtT\bar{R}_{\text{arith}} = \frac{\sum R_t}{T}
    • Geometric Mean (Compound Annual Growth Rate - CAGR): Measures the compound rate of return earned per period over a multi-period holding horizon:
      Rˉgeom=[(1+R1)(1+R2)…(1+RT)]1T−1\bar{R}_{\text{geom}} = \left[ (1 + R_1)(1 + R_2) \dots (1 + R_T) \right]^{\frac{1}{T}} - 1
    • Mathematical Relationship: Rˉgeom≈Rˉarith−12σ2\bar{R}_{\text{geom}} \approx \bar{R}_{\text{arith}} - \frac{1}{2}\sigma^2. The geometric mean is always less than or equal to the arithmetic mean, with the divergence widening as return volatility increases.

Core Concepts and Terminology: The Investment Environment

  • Real Asset vs Financial Asset: Real assets are tangible productive resources (factories, land) that generate goods and services in an economy. Financial assets are paper or digital claims (stocks, bonds) to the income generated by real assets.
  • Asset Allocation vs Security Selection: Asset allocation is the top-level choice of how much capital to invest across broad asset classes (stocks, bonds, cash). Security selection is the choice of specific individual securities within each designated class.
  • Arithmetic vs Geometric Mean Return: The arithmetic mean is the simple average of periodic returns, suitable for forecasting next period’s performance. The geometric mean is the compounded growth rate, reflecting the true multi-period growth of wealth.

Numerical Illustration 1: Holding Period Return and Annualized Yield Computation

Problem Statement: An investor on the Nepal Stock Exchange (NEPSE) purchases 500 common shares of Sanima Hydro-Power Ltd. on 1st Shrawan 2080 at Rs. 240 per share. During the holding period, the investor experiences the following cash flows:

  • On 15th Poush 2080 (Day 165), the company distributes a cash dividend of Rs. 18 per share.
  • On 1st Baisakh 2081 (Day 270), the investor sells all 500 shares at the prevailing NEPSE market price of Rs. 285 per share.

Required:

  1. Calculate the Total Initial Investment Outlay.
  2. Calculate the Capital Gains Yield, Dividend Yield, and Total Holding Period Return (HPR) in percentage and rupees.
  3. Compute the Annualized Holding Period Return (APR) and Effective Annualized Rate (EAR) assuming 365 days in a year.
  4. If the investor had purchased the shares on 50% margin borrowing at 12% annual interest, compute the leveraged HPR.

Step-by-Step Solution:

1. Initial Outlay:

Total Purchase Outlay=500 shares×Rs. 240=Rs. 120,000\text{Total Purchase Outlay} = 500 \text{ shares} \times \text{Rs. } 240 = \mathbf{\text{Rs. } 120,000}

2. Holding Period Return Components (270-Day Horizon):

  • Total Cash Dividends Received = 500×Rs. 18=Rs. 9,000500 \times \text{Rs. } 18 = \text{Rs. } 9,000.
  • Total Gross Sales Proceeds = 500×Rs. 285=Rs. 142,500500 \times \text{Rs. } 285 = \text{Rs. } 142,500.
  • Capital Gain = 142,500−120,000=Rs. 22,500142,500 - 120,000 = \text{Rs. } 22,500.
    Capital Gains Yield=285−240240=45240=18.75%\text{Capital Gains Yield} = \frac{285 - 240}{240} = \frac{45}{240} = \mathbf{18.75\%}
    Dividend Yield=18240=7.50%\text{Dividend Yield} = \frac{18}{240} = \mathbf{7.50\%}
    Total HPR=18.75%+7.50%=26.25%\text{Total HPR} = 18.75\% + 7.50\% = \mathbf{26.25\%}
    Total Rupee Profit=22,500+9,000=Rs. 31,500\text{Total Rupee Profit} = 22,500 + 9,000 = \mathbf{\text{Rs. } 31,500}

3. Annualized Return Computation (Holding Period = 270 days):

  • Nominal Annualized Return (APR):
    APR=HPR×(365n)=26.25%×(365270)=26.25%×1.35185=35.49%\text{APR} = \text{HPR} \times \left( \frac{365}{n} \right) = 26.25\% \times \left( \frac{365}{270} \right) = 26.25\% \times 1.35185 = \mathbf{35.49\%}
  • Effective Annual Rate (EAR):
    EAR=(1+HPR)365n−1=(1+0.2625)365270−1=(1.2625)1.35185−1=1.3739−1=37.39%\text{EAR} = (1 + \text{HPR})^{\frac{365}{n}} - 1 = (1 + 0.2625)^{\frac{365}{270}} - 1 = (1.2625)^{1.35185} - 1 = 1.3739 - 1 = \mathbf{37.39\%}

4. Leveraged Return with 50% Margin:

  • Own Equity Invested = 50%×120,000=Rs. 60,00050\% \times 120,000 = \text{Rs. } 60,000.
  • Borrowed Margin Funds = Rs. 60,000 at 12% p.a.
  • Margin Interest for 270 days = 60,000×12%×(270365)=Rs. 5,326.0360,000 \times 12\% \times \left( \frac{270}{365} \right) = \text{Rs. } 5,326.03.
    Net Leveraged Profit=31,500−5,326.03=Rs. 26,173.97\text{Net Leveraged Profit} = 31,500 - 5,326.03 = \text{Rs. } 26,173.97
    Leveraged HPR=Rs. 26,173.97Rs. 60,000=43.62%\text{Leveraged HPR} = \frac{\text{Rs. } 26,173.97}{\text{Rs. } 60,000} = \mathbf{43.62\%}
    Using 50% margin leverage amplifies the 270-day return from 26.25% up to 43.62%.

Numerical Illustration 2: Arithmetic Mean vs Geometric Mean Return Analysis

Problem Statement: A mutual fund portfolio in Nepal records the following annual returns over five consecutive fiscal years:

Fiscal Year Annual Return (RtR_t) Ending Wealth Multiplier (1+Rt1 + R_t)
Year 1 +35.0% 1.35
Year 2 -20.0% 0.80
Year 3 +25.0% 1.25
Year 4 +15.0% 1.15
Year 5 -10.0% 0.90

An investor placed Rs. 1,000,000 in this portfolio at the beginning of Year 1.

Required:

  1. Calculate the Arithmetic Mean Annual Return (Rˉarith\bar{R}_{\text{arith}}).
  2. Calculate the Geometric Mean Annual Return (Rˉgeom\bar{R}_{\text{geom}} / CAGR).
  3. Compute the actual portfolio wealth at the end of Year 5.
  4. Demonstrate why using the Arithmetic Mean to project cumulative wealth over 5 years is misleading and overstates ending wealth.

Step-by-Step Solution:

1. Arithmetic Mean Return:

Rˉarith=35.0−20.0+25.0+15.0−10.05=45.0%5=9.00% per year\bar{R}_{\text{arith}} = \frac{35.0 - 20.0 + 25.0 + 15.0 - 10.0}{5} = \frac{45.0\%}{5} = \mathbf{9.00\% \text{ per year}}

2. Geometric Mean Return (CAGR):

Cumulative Wealth Multiplier=1.35×0.80×1.25×1.15×0.90\text{Cumulative Wealth Multiplier} = 1.35 \times 0.80 \times 1.25 \times 1.15 \times 0.90
Multiplier=1.08×1.4375×0.90=1.5525×0.90=1.39725\text{Multiplier} = 1.08 \times 1.4375 \times 0.90 = 1.5525 \times 0.90 = \mathbf{1.39725}
Rˉgeom=(1.39725)1/5−1=(1.39725)0.20−1=1.06918−1=6.92% per year\bar{R}_{\text{geom}} = (1.39725)^{1/5} - 1 = (1.39725)^{0.20} - 1 = 1.06918 - 1 = \mathbf{6.92\% \text{ per year}}

3. Actual Ending Portfolio Wealth:

Ending Wealth=Initial Investment×1.39725=1,000,000×1.39725=Rs. 1,397,250\text{Ending Wealth} = \text{Initial Investment} \times 1.39725 = 1,000,000 \times 1.39725 = \mathbf{\text{Rs. } 1,397,250}

4. The Arithmetic Mean Distortion: If an analyst mistakenly compounds wealth using the Arithmetic Mean (9.00%):

Projected Wealth=1,000,000×(1+0.09)5=1,000,000×1.538624=Rs. 1,538,624\text{Projected Wealth} = 1,000,000 \times (1 + 0.09)^5 = 1,000,000 \times 1.538624 = \mathbf{\text{Rs. } 1,538,624}
Overstatement Error=1,538,624−1,397,250=Rs. 141,374 (Overstated by 10.12%)\text{Overstatement Error} = 1,538,624 - 1,397,250 = \mathbf{\text{Rs. } 141,374 \text{ (Overstated by 10.12\%)}}
Because returns fluctuated between +35% and -20%, compounding through volatility erodes compound wealth. The Geometric Mean (6.92%) correctly reflects the actual compounded growth rate, while the Arithmetic Mean (9.00%) creates an illusion of excess wealth.

Investment Analysis & Risk Caution: In TU examination evaluations, students often confuse investing (long-term fundamental commitment based on intrinsic value) with speculation (short-term price betting).

Paper Khoj independent study notes — unreviewed draft, not affiliated with Tribhuvan University.