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FIN 212

Investment Analysis and Portfolio Management

TU BBA-F · Semester 7 · BBA-F curriculum (2021 Common Core)

Requirement
elective
Credits
3
Study Guide
8 units available

Chapter notes

Authoritative study guide across 8 syllabus units

Open a unit to read its study notes.

Unit 1: Investment Setting· 3 LHs· ~4 marks

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Investment Setting

Investment Framework, Holding Period Returns, and Real Risk-Free Rates

Holding Period Return (HPR)

The total return earned on an asset over the entire duration it was held: HPR=P1−P0+D1P0=Ending Price−Beginning Price+Cash DividendBeginning Price\text{HPR} = \frac{P_1 - P_0 + D_1}{P_0} = \frac{\text{Ending Price} - \text{Beginning Price} + \text{Cash Dividend}}{\text{Beginning Price}}.

Real Risk-Free Rate (RRFRRRFR)

The pure time value of money under zero inflation and zero default risk, reflecting society’s baseline time preference for immediate consumption over future consumption.

Determinants of Required Return

Nominal Risk-Free Rate (NRFR)=(1+RRFR)(1+IP)−1≈RRFR+IP\text{Nominal Risk-Free Rate } (NRFR) = (1 + RRFR)(1 + IP) - 1 \approx RRFR + IP
Required Return (k)=NRFR+Business Risk+Financial Risk+Liquidity Risk+Exchange Risk\text{Required Return } (k) = NRFR + \text{Business Risk} + \text{Financial Risk} + \text{Liquidity Risk} + \text{Exchange Risk}

Components of Return and Multi-Period Compounding Dynamics

Structural Measurement of Multi-Period Returns

  1. Arithmetic Mean Return (AM):
    AM=∑t=1nRtn\text{AM} = \frac{\sum_{t=1}^n R_t}{n}
    Appropriate for estimating the expected return in any single subsequent period.
  2. Geometric Mean Return (GM) / Compound Annual Growth Rate (CAGR):
    GM=[∏t=1n(1+Rt)]1/n−1=[(1+R1)(1+R2)…(1+Rn)]1/n−1\text{GM} = \left[ \prod_{t=1}^n (1 + R_t) \right]^{1/n} - 1 = \left[ (1+R_1)(1+R_2)\dots(1+R_n) \right]^{1/n} - 1
    Appropriate for evaluating multi-year compounding performance. GM≤AM\text{GM} \le \text{AM}, with equality holding only if returns across all periods are identical.

Comparative Analysis: Arithmetic Mean vs Geometric Mean Returns

Measure Arithmetic Mean (AM) Geometric Mean (GM)
Formula 1n∑Rt\frac{1}{n} \sum R_t [∏(1+Rt)]1/n−1[\prod(1 + R_t)]^{1/n} - 1
Best Used For Forecasting single next-period future returns Measuring historical multi-year wealth accumulation
Volatility Distortion Distorted upwards by high variance True compounding growth rate; unaffected by variance bias

Multi-Period Return Computations and Risk-Adjusted Yield Analysis

Applied Problem: Multi-Period Arithmetic vs Geometric Return

An investor bought a stock on NEPSE for Rs. 400. Over 3 years, the stock returns were:

  • Year 1: +50%+50\% (Price rose to Rs. 600)
  • Year 2: −40%-40\% (Price fell to Rs. 360)
  • Year 3: +25%+25\% (Price rose to Rs. 450)
  1. Calculate the Arithmetic Mean annual return.
  2. Calculate the Geometric Mean annual return.
  3. Compute the total 3-year Holding Period Return (HPR).

Solution:

  1. Arithmetic Mean:
    AM=0.50+(−0.40)+0.253=0.353=11.67%\text{AM} = \frac{0.50 + (-0.40) + 0.25}{3} = \frac{0.35}{3} = 11.67\%
  2. Geometric Mean:
    1+R1=1.50,1+R2=0.60,1+R3=1.251 + R_1 = 1.50, \quad 1 + R_2 = 0.60, \quad 1 + R_3 = 1.25
    Product=1.50×0.60×1.25=1.125\text{Product} = 1.50 \times 0.60 \times 1.25 = 1.125
    GM=(1.125)1/3−1=1.04004−1=4.004%\text{GM} = (1.125)^{1/3} - 1 = 1.04004 - 1 = 4.004\%
  3. Total Holding Period Return (HPR):
    HPR=450−400400=50400=12.50%\text{HPR} = \frac{450 - 400}{400} = \frac{50}{400} = 12.50\%
    Notice that (1+0.04004)3−1=1.125−1=12.50%(1 + 0.04004)^3 - 1 = 1.125 - 1 = 12.50\%. The arithmetic mean (11.67%11.67\%) grossly overstates the investor’s actual compounding experience of 4.00%4.00\% per annum.

Key analytical nuance: they report the arithmetic average as the annual compound growth rate, masking the severe negative drag of the -40% year.