Investment Planning Flashcards
An investor has $10,000 to invest in a term deposit at 12% interest, paid semi-annually, for a 5 year period. What is the future value of this investment?
12% paid semi-annually
CPT FV
10000 ± PV
6 I/Y
10 N
0 PMT
CPT FV = 17,908
Real Rate of Return
R = (Nominal rate of return - Inflation rate) / (1 + Inflation rate)
Example:
5% annual interest rate on a term deposit, CPI is 2%, real rate of return:
R = (5% - 2%) / (1 + 2%) = 0.0294
Arithmetic Mean Return (Simple Average Return)
Arithmetic Mean Return = Sum of returns / numbers of observations
Geometric Mean Return
几何平均收益率
GMR = [(1 + R1)(1 + R2) … (1 + Rn)] ^ 1/n - 1
Example:
Portfolio returns in past 4 years: 22%, -17%, 42%, -7%
GMR = [(1.22) (0.83) (1.42) (0.93)] ^1/4 -1
= 1.337 ^ 0.25 - 1
= 7.53%
TI BALL Plus: 1.337 yx 0.25
Internal Rate of Return (IRR) = Dollar-Weighted Return = Money-Weighted Return
Clear calculator [ CF 2nd CLR WORK]
CF 8,000 ± Enter
↓ 0 Enter
↓↓ 2,000 ± Enter
↓↓ 0 Enter
↓↓ 19470 Enter
IRR CPT = 20.002
Time-Weighted Rate of Return
Year 1 return: (10000 - 8000) / 8000 = 0.25
Year 2 return: (12000 - 10000) / 10000 = 0.2
Year 3 return: (17000 - 14000) / 14000 = 0.2143
Year 4 return: (19470 - 17000) / 17000 = 0.1453
Annual geometric time weighted return:
= [(1.25) (1.2) (1.2143) (1.1453)] ^ 1/4 - 1
= 2.085 ^ 0.25 - 1
= 20.2%
Effective, Annual Rate of Return
Effective Annual Rate = (1 + Period return) ^ number of compounding periods - 1
Example 1:
A return of 12% per year on an investment compounded quarterly. Calculate the effective, annual rate of return
Step 1: convert the annual rate to a quarterly rate
12% / 4 = 0.03
Step 2: A $1.00 investment for 3 months would grow to $1 + 0.03 = $1.03
Effective Annual Rate of Return = 1.03 ^ 4 - 1 = 12.55%
Effective Annual Rate = (1 + Period return) ^ number of compounding periods - 1
Example 2:
Borrow money at an 8% annual interest rate; interest is compounded monthly. What is the effective annual yield.
Step 1: covert the annual rate to a monthly rate
8% / 12 = 0.006667
Step 2: A $1.00 investment for one month would grow to $1.006667
Effective Annual Rate of Return = 1.006667 ^ 12 - 1 = 8.3%
Constant Dividend Discount Model
PV = d1 / (r - g)
PV = Next period’s dividend / (Required return - Expected growth rate of dividend payments)
Example:
ABC common shares are expected to pay an annual dividend of $1.00 per share beginning the next period. The dividend should grow at an annual rate of 5%. The required rate of return on the shares is 15%. What is the present value of the stock?
PV = $1 / (0.15 - 0.05) = $10.00 per share
Measures of Central Tendency 集中趋势
Mean
- The arithmetic average of the data 平均数
Median
- The observation that falls in the middle of the data 中数
Mode
The observation that occurs with the greatest frequency 众数
Measures of Dispersion 离散量度 / 量度离差
Range
The difference between the highest value and lowest value in the observations
Variance 方差
The variance shows how much the observations vary from the mean
All differences are squared, then divided by the number of observations
Variance
σ² = [(X1−μ)² + (X2−μ)² + … + (Xn−μ)²] / n
μ = mean
Example:
Portfolio return 20%, 32%, 35%, -15%, - 22%
Mean = (20 + 32+ 35 - 15 - 22) / 5 = 10
Variance = [(20-10)² + (32-10)² + (35-10)² + (-15-10)² + (-22-10)²] / 5
= (100 + 484 + 625 + 625 + 1024) / 5
= 571.6
Standard Deviation 标准差 / 标准方差
- Square foot of variance
Standard deviation = √571.6 = 23.9%
The Empirical Rule
经验法则：统计学中的一种规律，即在正态分布中，
约 68% 的数据落在平均值的一个标准差范围内，
约 95% 的数据落在两个标准差范围内，
约 99% 的数据落在三个标准差范围内。
- 68% of all observations should fall within one standard deviation of the mean
- 95% of all observations should fall within two standard deviation of the mean
- 99% of all observations should fall within three standard deviation of the mean
Strategic Asset Allocation
- Fixed percentage weightings of the client’s asset allocation
- E.g. 5% cash, 30% fixed income, 65% equity
- There are long term targets
Dynamic Asset Allocation
Represents a rebalancing strategy, for investors, to get back to their long term strategic asset allocation
Tactical Asset Allocation
The portfolio manager is allowed to tilt the portfolio away from the long term strategic targets, to take advantage of short-term opportunities
Individuals and Life-Cycle Analysis
- Accumulation
○ Early to middle working years
○ Few assets and significant debts
○ Investment objectives include liquidity and growth - Consolidation
○ Well-established career
○ Debt has been paid down or eliminated
○ Growth is a major investment objective
○ Portfolio should be adjusted portion of fixed-income securities - Financial Independence
○ Retirement years where company pensions, government benefits and investment income are used to meet living expenses
○ Investment primarily in safety and income
○ Blue chip securities - Gifting
Pass on assets (family, charities), set up trusts
Investment Policy Statement (IPS)
- The IPS outlines significant aspects of the investment plan for the investor
- The main advantage of IPS is that it protects the portfolio from an arbitrary deviation from sound long-term policy
Efficient Market Hypothesis
The stock market is efficient and it is not possible, in the long run, to outperform the market
Weak form
- Suggest that market prices of stocks have no relation to past prices behavior
- Technical analysis is useless
- It is possible to profit only from fundamental analysis of all relevant publicly available information
Semi-strong form
- Suggests that stock prices reflect all publicly available information
- Both technical and fundamental analyses of public information are useless
- Only private (inside) information is useful
Strong form
- Suggest the stock prices reflect all publicly and privately available information
- Because the stock price reflects every single piece of information, there is absolutely no value in any type of analysis
Refuting the Efficient Market Theory
- January Effect
Shares of small capitalized companies have shown above-average risk-adjusted returns in January - Small Company Effect
Shares of smaller capitalization companies (small cap stocks), have shown above-average risk-adjusted returns - Price Earnings Effect (P/E)
Shares of companies with low P/Es have outperformed shares with high P/Es on a risk-adjusted basis, over long periods of time
