Fundamentals of Investment 2077 Board Question Paper

Individual Investors vs. Institutional Investors

1. Investment Scale & Resources: Individual investors invest personal wealth with limited research budgets, whereas institutional investors (mutual funds, CIT, EPF, life insurance firms) pool billions with dedicated research desks.
2. Horizon & Liquidity Needs: Individuals often face personal lifecycle liquidity constraints (education, home purchase); institutions have predictable actuarial liability horizons allowing long-term asset-liability matching.
3. Regulatory Scrutiny: Institutional investors are subject to stringent fiduciary mandates and statutory prudential investment guidelines.

Why Short Selling is More Risky Than Long Purchase

• Long Purchase: Maximum potential loss is limited to the initial purchase price ($100\%$ of invested capital, as stock cannot drop below zero), while upside potential is theoretically infinite.
• Short Sale: Potential loss is theoretically infinite because the stock price can rise indefinitely without ceiling, while maximum profit is capped at the initial short sale price (if stock falls to zero). Furthermore, short sellers face margin calls and forced buy-ins.

Margin Call Price on Short Sale:

• Initial Price ($P_0$) = $\text{Rs. } 200$
• Initial Margin ($IM$) = $55\% = 0.55$
• Maintenance Margin ($MM$) = $25\% = 0.25$$P^* = \frac{P_0 (1 + IM)}{1 + MM} = \frac{200 (1 + 0.55)}{1 + 0.25} = \frac{310}{1.25} = \mathbf{\text{Rs. } 248}$$ Conclusion: A margin call will be triggered if the stock price rises to Rs. 248 per share.

Market Order vs. Limit Order

• Market Order: An order to buy or sell a security immediately at the best available prevailing market price; prioritizes certainty and speed of execution over price.
• Limit Order: An order to buy at or below a specified limit price, or sell at or above a specified limit price; prioritizes price certainty but execution is not guaranteed if market moves away.

Yield on Investment:

• $PV = \text{Rs. } 6,000$, $FV = \text{Rs. } 10,500$, $n = 9$ years.
  $$FV = PV(1 + r)^n \implies 1 + r = \left(\frac{10,500}{6,000}\right)^{1/9} = (1.75)^{0.111111} = 1.0642$$
  $$r = 1.0642 - 1 = \mathbf{6.42\%}$$
  Recommendation: Reject this investment because the realized yield (6.42%) is lower than the required minimum return of 7.0%.

Meaning of Reinvestment Risk

Reinvestment risk is the uncertainty that future intermediate cash flows (such as semi-annual bond coupon payments) will have to be reinvested at an interest rate lower than the bond’s original Yield to Maturity (YTM) at purchase. It is highest for high-coupon, callable, and short-maturity bonds in declining rate environments.

Calculation of Bond Price:

• Par Value ($M$) = $\text{Rs. } 1,000$, Coupon Rate = $8\% \implies I = \text{Rs. } 80$.
• Term ($n$) = 10 years, Market YTM ($k_d$) = $10\%$.
  $$V_B = I(PVIFA_{10\%, 10}) + M(PVIF_{10\%, 10})$$
  $$PVIFA_{10\%, 10} = 6.14457, \quad PVIF_{10\%, 10} = 0.38554$$
  $$V_B = (80 \times 6.14457) + (1,000 \times 0.38554) = 491.57 + 385.54 = \mathbf{\text{Rs. } 877.11}$$
  Conclusion: The price of the bond will be Rs. 877.11 (sells at a discount since coupon < YTM).

Closed-End Fund Share Market Price:

• Total Assets = $\text{Rs. } 1,000\text{M}$, Liabilities = $\text{Rs. } 5\text{M}$, Shares = $50\text{M}$.
  $$NAV = \frac{1,000\text{M} - 5\text{M}}{50\text{M}} = \frac{995\text{M}}{50\text{M}} = \mathbf{\text{Rs. } 19.90}$$
• Market Price at $5\%$ Discount:
  $$P = NAV(1 - \text{Discount}) = 19.90 \times (1 - 0.05) = 19.90 \times 0.95 = \mathbf{\text{Rs. } 18.905}$$
  Conclusion: The market price of the fund’s shares is Rs. 18.91.

Interpretation of Jensen’s Alpha = +0.90%

Jensen’s Alpha ($\alpha_p$) measures the risk-adjusted abnormal excess return earned by a portfolio over and above what is predicted by the Capital Asset Pricing Model (CAPM).

• An alpha of +0.90% indicates that the portfolio manager generated a positive abnormal return of 0.90% per year due to superior stock selection or market timing skills after controlling for systematic market risk (beta).

Intrinsic Value of Call Option:

• Current Stock Price ($S$) = $\text{Rs. } 212$
• Strike Price ($X$) = $\text{Rs. } 200$
• Premium Paid = $\text{Rs. } 5$$\text{Intrinsic Value per Share} = \max(0, S - X) = \max(0, 212 - 200) = \mathbf{\text{Rs. } 12}$$
• For 100 shares: $100 \times 12 = \mathbf{\text{Rs. } 1,200}$. (Net Profit = $\text{Rs. } 12 - \text{Rs. } 5 = \text{Rs. } 7$ per share).

Features, Advantages, and Disadvantages of Options

1. Basic Features:
   • Call Option: Grants the holder the right (not obligation) to purchase an underlying stock at a specified strike price on or before maturity.
   • Put Option: Grants the holder the right (not obligation) to sell an underlying stock at a specified strike price on or before maturity.
2. Advantages:
   • Substantial financial leverage with minimal upfront capital.
   • Defined, limited downside risk (maximum loss is premium paid).
   • Versatile hedging tools against market downturns.
3. Disadvantages:
   • Time decay (theta): Options are wasting assets that expire worthless if unexercised.
   • High complexity and volatility.

Margin Purchase Analysis for Subham Hamal:

• Purchased 500 shares at Rs 400. Initial Value $= 500 \times 400 = \text{Rs. } 200,000$.
• Initial Margin ($IM$) = $50\%$, Maintenance Margin ($MM$) = $25\%$.
• Dividend $= \text{Rs. } 11$/share. Loan Interest $= 8\%$ p.a., Holding Period = 4 months.

---

a. Initial Transaction Breakdown:

• Total Initial Value: $\mathbf{\text{Rs. } 200,000}$
• Initial Equity: $200,000 \times 0.50 = \mathbf{\text{Rs. } 100,000}$
• Debit Balance (Margin Loan): $200,000 - 100,000 = \mathbf{\text{Rs. } 100,000}$

---

b. Stock Price Rises to Rs. 700:

• Market Value of Stock $= 500 \times 700 = \text{Rs. } 350,000$.
• Equity Position $= 350,000 - 100,000 = \text{Rs. } 250,000$.
• Actual Margin Percentage:
  $$AM = \frac{\text{Equity}}{\text{Market Value}} = \frac{250,000}{350,000} = 0.7143 = \mathbf{71.43\%}$$
• Account Status: Since Actual Margin ($71.43\%$) exceeds Initial Margin ($50\%$), the account has excess equity of $\text{Rs. } 250,000 - (350,000 \times 0.50) = \mathbf{\text{Rs. } 75,000}$.

---

c. Dividends Received and Interest Paid (4 Months):

• Total Dividend Received $= 500 \times 11 = \mathbf{\text{Rs. } 5,500}$.
• Interest on Margin Loan $= 100,000 \times 8\% \times \frac{4}{12} = \mathbf{\text{Rs. } 2,666.67}$.

Interpretation of Financial Newspaper Stock Quote (Mega Stock):

Given row: 52-Week Hi: 425 | Lo: 392 | Stock: Mega | Div: 12.25 | Yld: 2.95% | PE: 15.30 | Vol: 536 | Close: 415 | Net Chg: -2

• a. Trading Day: Trading occurred on the business day prior to the publication date (i.e., Monday, February 5).
• b. P/E Ratio: 15.30. This indicates investors are willing to pay Rs 15.30 for every Rs 1 of Mega’s trailing earnings.
• c. Last Trading Price: Rs. 415.
• d. Expected Dividend: Rs. 12.25 per share.
• e. 52-Week High and Low: High = Rs. 425, Low = Rs. 392.
• f. Trading Volume: $536 \times 100 = \mathbf{53,600 \text{ shares}}$.
• g. Immediately Preceding Close: $\text{Close} - \text{Net Chg} = 415 - (-2) = \mathbf{\text{Rs. } 417}$.

Holding Period Return on Mutual Fund Investment:

Given: Offering Price $P_0 = \text{Rs. } 16$ ($NAV_0 = \text{Rs. } 15$), Year 1 Distributions $D_1 = \text{Rs. } 2$, Ending $NAV_1 = \text{Rs. } 18$.

• a. HPR with Load Fee (Purchased at Offering Price Rs 16):

  $$HPR = \frac{NAV_1 - P_0 + D_1}{P_0} = \frac{18 - 16 + 2}{16} = \frac{4}{16} = 0.25 = \mathbf{25.0\%}$$

• b. HPR with No-Load Fee (Purchased at NAV Rs 15):

  $$HPR = \frac{NAV_1 - NAV_0 + D_1}{NAV_0} = \frac{18 - 15 + 2}{15} = \frac{5}{15} = 0.3333 = \mathbf{33.33\%}$$

• c. HPR with Reinvestment at Rs. 16/share:

  • Initial 100 shares cost Rs 1,600. Cash distributions $= 100 \times 2 = \text{Rs. } 200$.
  • Additional shares acquired $= \frac{200}{16} = 12.5 \text{ shares}$.
  • Total ending shares $= 112.5 \text{ shares}$.
  • Ending Value $= 112.5 \times 18 = \text{Rs. } 2,025$.
    $$HPR = \frac{2,025 - 1,600}{1,600} = \frac{425}{1,600} = 0.2656 = \mathbf{26.56\%}$$

Evaluation of Portfolios P, Q, R, S:

Assume standard risk-free rate $R_f = 6\%$.

• Sharpe Ratio: $S_p = \frac{\bar{R}_p - R_f}{\sigma_p}$
  • $S_P = \frac{19 - 6}{14} = \frac{13}{14} = \mathbf{0.929}$
  • $S_Q = \frac{14.5 - 6}{12} = \frac{8.5}{12} = \mathbf{0.708}$
  • $S_R = \frac{14 - 6}{9} = \frac{8}{9} = \mathbf{0.889}$
  • $S_S = \frac{11 - 6}{10} = \frac{5}{10} = \mathbf{0.500}$
• Treynor Ratio: $T_p = \frac{\bar{R}_p - R_f}{\beta_p}$
  • $T_P = \frac{13}{1.2} = \mathbf{10.83\%}$
  • $T_Q = \frac{8.5}{1.1} = \mathbf{7.73\%}$
  • $T_R = \frac{8}{1.3} = \mathbf{6.15\%}$
  • $T_S = \frac{5}{1.0} = \mathbf{5.00\%}$ Conclusion: Portfolio P ranks #1 across both total risk (Sharpe = 0.929) and systematic risk (Treynor = 10.83%).

Major Types of Investment Vehicles & Prevalence in Nepal

1. Major Global Investment Vehicles:
   • Equity Securities: Common stock and preferred stock.
   • Fixed Income Securities: Treasury bills, government development bonds, corporate debentures.
   • Collective Investment Schemes: Mutual funds (open-end & closed-end), ETFs.
   • Derivative Instruments: Options, futures, swaps.
   • Real Assets: Real estate, gold, commodities.
2. Most Common Vehicles in Nepalese Financial Market:
   • Common Stocks (Equities): Dominates over $80\%$ of secondary market turnover on NEPSE, driven by commercial banks, insurance, and hydropower IPOs via C-ASBA.
   • Mutual Funds: Growing popularity with dozens of closed-end and open-end schemes offering retail diversification.
   • Corporate Debentures & Bank Fixed Deposits: Preferred by risk-averse savers for guaranteed yields.

Two-Stock Portfolio Risk and Return Analysis:

Given equal investment ($w_X = 0.5$, $w_Y = 0.5$):

• State 1 ($P_1 = 0.3$): $R_X = -10\%$, $R_Y = 20\%$
• State 2 ($P_2 = 0.4$): $R_X = 5\%$, $R_Y = 10\%$
• State 3 ($P_3 = 0.3$): $R_X = 15\%$, $R_Y = 5\%$

---

a. Expected Returns and Standard Deviations:

• Stock X:

  $$E(R_X) = (0.3 \times -10) + (0.4 \times 5) + (0.3 \times 15) = -3 + 2 + 4.5 = \mathbf{3.5\%}$$
  $$\sigma_X^2 = 0.3(-10 - 3.5)^2 + 0.4(5 - 3.5)^2 + 0.3(15 - 3.5)^2 = 0.3(182.25) + 0.4(2.25) + 0.3(132.25) = 54.675 + 0.9 + 39.675 = \mathbf{95.25}$$
  $$\sigma_X = \sqrt{95.25} = \mathbf{9.76\%}$$

• Stock Y:

  $$E(R_Y) = (0.3 \times 20) + (0.4 \times 10) + (0.3 \times 5) = 6 + 4 + 1.5 = \mathbf{11.5\%}$$
  $$\sigma_Y^2 = 0.3(20 - 11.5)^2 + 0.4(10 - 11.5)^2 + 0.3(5 - 11.5)^2 = 0.3(72.25) + 0.4(2.25) + 0.3(42.25) = 21.675 + 0.9 + 12.675 = \mathbf{35.25}$$
  $$\sigma_Y = \sqrt{35.25} = \mathbf{5.94\%}$$

---

b. Covariance and Correlation Coefficient:

$$Cov(X, Y) = \sum P_i [R_{Xi} - E(R_X)][R_{Yi} - E(R_Y)]$$

$$Cov(X, Y) = 0.3(-13.5)(8.5) + 0.4(1.5)(-1.5) + 0.3(11.5)(-6.5) = -34.425 - 0.9 - 22.425 = \mathbf{-57.75}$$

$$\rho_{XY} = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} = \frac{-57.75}{9.76 \times 5.94} = \frac{-57.75}{57.9744} = \mathbf{-0.996}$$

---

c. Diversification Effect:

Yes, magnificent diversification! Since $\rho_{XY} \approx -1.0$, the stocks move in nearly perfect opposite directions, virtually eliminating all unsystematic portfolio variance.

---

d. Portfolio Return and Risk:

$$E(R_p) = (0.5 \times 3.5\%) + (0.5 \times 11.5\%) = 1.75 + 5.75 = \mathbf{7.50\%}$$

$$\sigma_p^2 = (0.5)^2(95.25) + (0.5)^2(35.25) + 2(0.5)(0.5)(-57.75) = 23.8125 + 8.8125 - 28.875 = \mathbf{3.75}$$

$$\sigma_p = \sqrt{3.75} = \mathbf{1.94\%}$$

(Notice portfolio risk drops to an astonishing 1.94%!).

---

e. Investor Preference:

Prefer the Portfolio. It yields a generous 7.50% return with minuscule risk (1.94%), far superior to holding high-risk Stock X alone.

Dividend Discount Model Analysis for JBL Company:

Given: $D_0 = \text{Rs. } 40$, $D_1 = \text{Rs. } 43.2$, $D_2 = \text{Rs. } 46.7$, $D_3 = \text{Rs. } 50.4$. Forecasted $P_3 = \text{Rs. } 777.50$, Current Price $P_0 = \text{Rs. } 565$, Required Return $k_s = 15\%$.

---

a. Intrinsic Value per Share ($k_s = 15\%$):

$$V_0 = \frac{D_1}{1 + k_s} + \frac{D_2}{(1 + k_s)^2} + \frac{D_3 + P_3}{(1 + k_s)^3}$$

$$V_0 = \frac{43.2}{1.15} + \frac{46.7}{(1.15)^2} + \frac{50.4 + 777.50}{(1.15)^3} = 37.565 + 35.312 + \frac{827.90}{1.520875} = 37.565 + 35.312 + 544.358 = \mathbf{\text{Rs. } 617.24}$$

---

b. Expected Return Using IRR:

Solve for $r$ where $PV(\text{Cash Flows}) = 565$:

$$565 = \frac{43.2}{1 + r} + \frac{46.7}{(1 + r)^2} + \frac{827.90}{(1 + r)^3} \implies r \approx \mathbf{18.4\%}$$

---

c. Constant Growth Model ($g = 8\%$, $k_s = 15\%$):

$$D_1 = 40(1 + 0.08) = \text{Rs. } 43.20$$

$$P_0 = \frac{D_1}{k_s - g} = \frac{43.20}{0.15 - 0.08} = \frac{43.20}{0.07} = \mathbf{\text{Rs. } 617.14}$$

---

d. Why $g$ Cannot Exceed $k_s$ in Constant Growth:

If $g \ge k_s$, the Gordon denominator $(k_s - g) \le 0$, yielding mathematically infinite or negative stock prices. Economically, no firm can grow perpetually faster than the overall macroeconomy without eventually becoming larger than the entire economy.

---

e. End of Year 3 Price ($P_3$):

$$D_4 = D_3(1 + g) = 50.40(1.08) = \text{Rs. } 54.432$$

$$P_3 = \frac{D_4}{k_s - g} = \frac{54.432}{0.15 - 0.08} = \frac{54.432}{0.07} = \mathbf{\text{Rs. } 777.60}$$

Conclusion: The calculated price of Rs. 777.60 matches the problem’s forecasted price of Rs. 777.50, confirming the analyst utilized the constant growth DDM to set the 3-year horizon price target.