Diversification

Show your work for each problem.

1.
What is the main purpose of diversification in investing?
1. a)To avoid paying taxes
2. b)To invest only in stocks
3. c)To reduce risk by spreading investments
4. d)To maximize returns at any cost
Answer: To reduce risk by spreading investments
Diversification's main purpose is to reduce risk by spreading investments across different asset types. When one investment falls, others may rise or stay stable.
2.
A portfolio has 60% stocks and 40% bonds. If all weights must sum to 100%, what is 0.60 + 0.40?
Answer: 1
, which equals 100%. Portfolio weights must always sum to 1 (or 100%).
3.
Which correlation value indicates the BEST diversification benefit?
1. a)+1.0
2. b)+0.8
3. c)+0.2
4. d)-0.5
Answer: -0.5
-0.5 indicates the best diversification because negative correlation means when one asset falls, the other tends to rise. This smooths out portfolio returns.
4.
Calculate the weighted return:
Answer: 5
. This means if 50% of your portfolio is in an asset with 10% return, it contributes 5% to your overall portfolio return.
5.
A portfolio has 60% stocks (8% return) and 40% bonds (4% return). Calculate the expected portfolio return.
Answer: 6.4
1. Calculate the stock contribution: 4.8
2. Calculate the bond contribution: 1.6
3. Add both contributions: 6.4
6.
Which portfolio is TRULY diversified?
1. a)50% Apple stock, 50% Microsoft stock
2. b)80% bank stocks, 20% insurance stocks
3. c)100% in 20 different tech companies
4. d)40% stocks, 30% bonds, 20% real estate, 10% gold
Answer: 40% stocks, 30% bonds, 20% real estate, 10% gold
Only the first option diversifies across different asset classes (stocks, bonds, real estate, commodities). The others all concentrate in one sector (tech or financial), which means they'll move together during market events.
7.
A portfolio has 70% stocks (10% return) and 30% bonds (4% return). What is the expected return in percent?
Answer: 8.2
8.
Calculate the expected return for a portfolio with: 50% US stocks (9%), 30% European stocks (6%), 20% bonds (3%).
Answer: 6.9
1. US stocks contribution: 4.5
2. European stocks contribution: 1.8
3. Bonds contribution: 0.6
4. Total expected return: 6.9
9.
Why should investors regularly rebalance their portfolios?
1. a)To maximize returns regardless of risk
2. b)To impress their friends
3. c)To maintain the intended risk level as assets grow at different rates
4. d)To avoid paying taxes
Answer: To maintain the intended risk level as assets grow at different rates
Rebalancing maintains your intended risk level. If a 60/40 portfolio becomes 80/20 due to stock growth, you're now taking more risk than planned. Rebalancing sells some winners and buys underperformers to restore the original allocation.
10.
An index fund has 30% tech (which falls 50%) and 70% other sectors (which stay flat). What is the fund's total percentage loss?
Answer: 15
1. What is the tech sector's loss contribution? 15
2. What is the other sectors' loss contribution? 0
3. What is the total fund loss? 15
11.
Portfolio A (100% stocks) returns: Year 1: +20%, Year 2: -30%, Year 3: +25%. If you start with 10,000 euros, what is your final amount (rounded to nearest euro)?
Answer: 10500
Year 1: . Year 2: . Year 3: euros.
12.
Portfolio B (50% stocks, 50% bonds) over 3 years: Stocks: +20%, -30%, +25%. Bonds: +4%, +5%, +3%. Starting with 10,000 euros, what is the final amount?
Answer: 10874
1. Stock portion after 3 years: 5250
2. Bond portion after 3 years: 5624
3. Total final amount: 10874
4. Portfolio B outperforms A by how many euros? 374
13.
Which risk can diversification NOT eliminate?
1. a)Systematic risk (market-wide recessions)
2. b)Currency risk in a single country
3. c)Risk specific to one company
4. d)Risk of one sector underperforming
Answer: Systematic risk (market-wide recessions)
Systematic risk affects all investments simultaneously (like a recession or financial crisis). Diversification can only reduce unsystematic risk - the risk specific to individual companies or sectors.
14.
If a portfolio has weights of 25%, 35%, and 40%, do they sum to 100%?
1. a)No, they sum to 110
2. b)Cannot be determined
3. c)Yes, 25 + 35 + 40 = 100
4. d)No, they sum to 90
Answer: Yes, 25 + 35 + 40 = 100
. This is a valid portfolio allocation because all weights sum to 100%.
15.
A diversified portfolio has: US 40% (-3% return), Europe 35% (+7% return), Asia 25% (+5% return). What is the overall return?
Answer: 2.5
. Geographic diversification turned a US loss into an overall gain!
16.
A 60/40 portfolio grows: stocks 60% → 75% of portfolio, bonds 40% → 25%. To rebalance back to 60/40 with 100,000 euros total, how much needs to move from stocks to bonds?
Answer: 15000
1. Current stock value (75% of 100,000)? 75000
2. Target stock value (60% of 100,000)? 60000
3. How much to sell from stocks? 15000
4. This amount moves to bonds. New bond value? 40000