Five HKSI Problem Explanations: From Simple Interest to Bonds

As HKSI exam-style questions often show, solid financial intuition beats memorization. Today we walk through five problems that touch on common topics in HKSI: simple interest, stamp duty on trades, yield curves, VaR (Value at Risk), and fixed-income maturity. The goal isn’t just to get the right letter but to understand the thinking behind each answer so you can apply these ideas in real-market contexts.

1) Simple interest: How long to grow an investment?

Question (paraphrased): If you invest HK$1,000,000 at a simple interest rate of 22厘 (0.22) per year, how many years will it take for the investment to reach HK$25,000,000?

Key idea:

• Under simple interest, the future value is: FV = P × (1 + r × t) where P is the principal, r is the annual rate (as a decimal), and t is time in years.
• Rearranging for t: t = (FV / P − 1) / r

Calculation:

• FV / P = 25,000,000 / 1,000,000 = 25
• FV / P − 1 = 24
• t = 24 / 0.22 ≈ 109.09 years

Answer: About 109 years.

What this teaches:

• With simple interest, the growth is linear in time. If you need a quick estimate of how long a simple-interest plan will take to reach a target, use t = (FV/P − 1)/r. Small changes in r or target can lead to large changes in t when the target is huge.

2) Stamp duty and trading costs in HK: What’s correct?

Question (paraphrased): Which statement about Hong Kong Exchange trading fees is correct?

Options summarize common misunderstandings, but the correct interpretation is:

• Stamp duty is paid by both the buyer and the seller for each trade. The rate on the stock transaction value is 0.1% (even if the calculation yields less than HK$1, it’s rounded up to HK$1).
• There is a separate stamp duty on stock transfer documents (transfer of shares) of HK$5 per instrument, paid by the seller, and it does not depend on the number of shares involved.
• For certain instruments like exchange-traded funds (ETFs), warrants, bull/bear products, and options, the stamp duty treatment differs from ordinary stock trading and may be exempted in some cases.

Why this matters for practitioners:

• Understanding who pays what helps in accurate cost calculations of trades and in pricing models that rely on net-of-fee assumptions.

Takeaway:

• In HK, stamp duty basics involve both buyer and seller paying 0.1% of the trade value, with a mandatory HK$5 per transfer document payable by the seller. ETFs and certain derivatives have nuanced rules, which is why exam questions emphasize the correct application rather than generic statements.

3) Yield curves: What does a single curve tell you?

Question (paraphrased): On the same yield curve, what prices different bonds on that curve?

Answer and explanation:

• A yield (or yield-to-m maturity) curve shows the yields of bonds in the same category (e.g., same credit quality), but across different maturities. The curve helps compare how price changes with maturity for bonds of the same risk class.
• Therefore, on one yield curve, you see the prices (or yields) of bonds from the same category but with different maturities.

Takeaway:

• The yield curve is a fundamental tool for assessing term structure risk and for pricing debt securities with different maturities within the same risk class.

4) VaR and confidence levels: Interpreting daily VaR

Question (paraphrased): If a trading book reports a daily VaR of HK$1,000,000 at a 90% confidence level, what does this imply about the probability of daily losses exceeding HK$1,000,000?

Answer and explanation:

• By definition, a 90% VaR means that in 10% of days you would expect the loss (or profit) to exceed the VaR threshold. Because losses and gains are typically considered in a left-tail sense for VaR, under a symmetric (approximately normal) distribution the probability that losses exceed HK$1,000,000 is about 5%.
• So the daily probability of a loss beyond HK$1,000,000 is 5% (the left tail beyond the VaR level in a symmetric distribution).

Takeaway:

• VaR tells you the threshold such that only a certain fraction of days fall outside it; the exact tail probability depends on the distribution shape, but for a 90% VaR under symmetry, the one-sided loss tail is about 5% in many practical approximations.

5) Fixed-income maturity terminology: What is a bond?

Question (paraphrased): If a fixed-rate security has a maturity generally between 2 and 10 years, what is it called?

Answer:

• Bond. In practice, securities with maturities in the 2–10 year range are typically referred to as bonds (as opposed to bills, which are shorter, or notes with different conventions).

Takeaway:

• Maturity range helps classify fixed-income instruments. Understanding these labels aids in selecting the right instrument for desired risk, duration, and yield profiles.

Wrapping up

These five problems touch on foundational HKSI content: time value of money under simple interest, the practicalities of stamp duties on trades, the informational role of the yield curve, risk quantification with VaR, and fixed-income naming conventions. By walking through the reasoning rather than only the final answer, you build a toolkit you can apply to real exam questions and market scenarios alike.

If you found this problem-focused walkthrough helpful, make sure to follow HKSIYES for more curated explanations and practice problems tailored for HKSI learners. We publish regular insights to help you stay ahead in HKSI exam preparation and market understanding.