Noesis
Interleaved — Phase 2

Stock-Market interleaved practice

printable — key stays hidden on paper

Instructions: Solve all problems. Show working for numerical questions. Use ...... for math notation. Each problem draws from a different subtopic — read carefully and pick the right concept/formula before computing. Total: 50 marks.

1. A 5-year bond has a face value of \1000,anannualcouponrateof, an annual coupon rate of 8%,andcurrentlytradesat, and currently trades at $1080$. Calculate its current yield (coupon yield), and state whether its yield-to-maturity is above or below the coupon rate. (5 marks)

2. An investor puts \60{,}000intoamutualfundwhentheNAVisinto a mutual fund when the NAV is$25.ThreemonthslatertheNAVrisesto. Three months later the NAV rises to $30$. How many units were bought, and what is the current value of the holding? (4 marks)

3. A zero-coupon bond with face value \1000maturesin4yearsandispricedtoyieldmatures in 4 years and is priced to yield6%$ annually (compounded annually). Compute its issue price. (5 marks)

4. Two funds track the same index. Fund A has an expense ratio of 0.10%0.10\% and tracking error of 0.15%0.15\%; Fund B has an expense ratio of 0.90%0.90\% and tracking error of 0.60%0.60\%. Explain which is preferable for a passive investor and why, referencing both metrics. (4 marks)

5. A government bond currently yields 7%7\%. Market interest rates rise to 8%8\%. Without exact calculation, state qualitatively what happens to the bond's price and why, naming the relationship involved. (4 marks)

6. A bond fund holds a portfolio with a modified duration of 6.56.5 years. If interest rates rise by 0.50%0.50\% (50 basis points), estimate the approximate percentage change in the fund's value. (5 marks)

7. Distinguish between a debenture and a convertible bond. For the convertible, if a \1000$ bond converts into 40 shares, what share price makes conversion worthwhile? (5 marks)

8. Gold trades at a spot price of \2000/oz.A6−monthfuturescontractispricedat/oz. A 6-month futures contract is priced at $2050$/oz. Assuming no storage/convenience adjustments, what does this pricing pattern indicate about the market (name it), and what is the implied annualized cost-of-carry? (6 marks)

9. Investor X does a lumpsum of \120{,}000;InvestorYdoesaSIPof; Investor Y does a SIP of $10{,}000$/month for 12 months. In a falling-then-rising (V-shaped) market, which approach tends to give a lower average cost per unit, and why? (4 marks)

10. A REIT distributes 90%90\% of its rental income and trades like a stock on an exchange. State two ways a REIT differs from a bond as an income asset, and one way it resembles equity. (4 marks)

Answer keyMark scheme & solutions

1. Subtopic 2.1.4 — Yield & YTM. Current yield =annual couponprice=801080=0.0741=7.41%= \dfrac{\text{annual coupon}}{\text{price}} = \dfrac{80}{1080} = 0.0741 = 7.41\%. Since the bond trades at a premium (1080>10001080 > 1000), the YTM is below the coupon rate (8%8\%). A premium bond's YTM < coupon rate < current yield... actually: coupon rate (8%8\%) > current yield (7.41%7.41\%) > YTM. YTM is below both. Why this method: "Current yield" uses only coupon/price; the premium tells you the YTM direction without solving the full YTM equation — distinguish the two yield measures.

2. Subtopic 2.2.1 — Mutual funds & NAV. Units =60000/25=2400= 60000 / 25 = 2400 units. Current value = 2400 \times 30 = \72{,}000$. Why: NAV is price per unit; units = investment/NAV, value = units×NAV. Not a yield problem — pick the NAV relationship.

3. Subtopic 2.1.10 — Zero-coupon bonds. Price = \dfrac{FV}{(1+r)^n} = \dfrac{1000}{(1.06)^4} = \dfrac{1000}{1.26247} = \792.09$. Why: No coupons → single discounting of face value only. Contrast with problem 1 (coupon bond).

4. Subtopic 2.2.4 — Expense ratios & tracking error. Fund A is preferable. Lower expense ratio (0.10%0.10\% vs 0.90%0.90\%) means more return retained; lower tracking error (0.15%0.15\% vs 0.60%0.60\%) means it follows the index more faithfully. For passive investing both metrics should be minimized — A wins on both. Why: Conceptual comparison, no formula; recognize the two distinct quality metrics for index funds.

5. Subtopic 2.1.5 — Inverse price-yield relationship. Bond price falls. When market rates rise above the bond's fixed coupon, existing bonds become less attractive, so their price must drop until their yield matches the new market rate. This is the inverse price-yield relationship. Why: Qualitative — recognize it's about direction, not duration magnitude (that's problem 6).

6. Subtopic 2.1.8 — Duration & rate sensitivity. %ΔP≈−Dmod×Δy=−6.5×0.005=−0.0325=−3.25%\%\Delta P \approx -D_{mod} \times \Delta y = -6.5 \times 0.005 = -0.0325 = -3.25\%. The fund loses approximately 3.25%3.25\%. Why: Duration quantifies sensitivity; problem 5 was direction only, this needs the modified-duration formula.

7. Subtopic 2.1.9 — Debentures & convertible bonds. A debenture is an unsecured debt instrument backed only by the issuer's creditworthiness (no specific collateral). A convertible bond additionally gives the holder the option to convert into a fixed number of equity shares. Conversion value =40×= 40 \times share price. Conversion beats holding the \1000bondwhenbond when40 \times P > 1000 \Rightarrow P > $25$. Why: Definition + break-even conversion price; identify the embedded equity option.

8. Subtopic 2.3.3 — Spot vs futures pricing. Futures (\2050)>spot() > spot ($2000)→marketisin∗∗contango∗∗.Carryover6months) → market is in **contango**. Carry over 6 months = 2050/2000 - 1 = 2.5%.Annualized. Annualized \approx 2.5% \times 2 = 5%(simple),or(simple), or(1.025)^2 - 1 = 5.06%$ compounded. Why: Recognize contango (futures above spot) vs backwardation; compute cost-of-carry. Distinguish commodity futures from bond pricing.

9. Subtopic 2.2.5 — SIP vs lumpsum. In a V-shaped (falls then rises) market, SIP gives a lower average cost per unit because rupee-cost averaging buys more units when prices are low. Lumpsum locks in the entry price at the top. SIP benefits from volatility on the way down. Why: Conceptual — recognize rupee-cost averaging advantage in dipping markets.

10. Subtopic 2.2.10 — REITs & InvITs. Differences from a bond: (i) REIT income (distributions) is not fixed/guaranteed — it varies with rental income; (ii) REITs have no maturity/face value and market price fluctuates like a share. Resemblance to equity: it trades on an exchange with price appreciation potential and represents ownership of underlying assets. Why: Position REIT as a hybrid income+equity asset, distinct from fixed-income bonds.

[
  {"claim":"Current yield of 8% coupon $1000 bond at price $1080 is 7.41%","code":"cy=80/1080; result=round(cy,4)==0.0741"},
  {"claim":"Zero-coupon bond FV 1000, 4yr, 6% yields price 792.09","code":"price=1000/(1.06**4); result=round(price,2)==792.09"},
  {"claim":"Modified duration 6.5, rate +0.5% gives -3.25% price change","code":"pct=-6.5*0.005; result=round(pct*100,2)==-3.25"}
]