无代写-7B
时间:2022-03-22
1
1/ 79
7B
2
Income
& Safety
Long Term
Capital
Appreciation
Liquidity & Security
Risk
Emergency Fund
Home
Money Market Funds
Life & Disability
Insurance
Bonds & Debentures
Bond & Mortgage Funds
Annuities
Preferred Shares
CSBs, GICs, T-Bills
Real Estate
Equity Funds
Common Stock
Art
Speculative Stocks
Gold & Silver
Speculative Funds
2/ 79
3Broad Types of Investments
Bond Markets
Money Markets
Equity Markets
Short Term Debt < 1 yrs, 3yrs
Maturities
Short Term < 3 years
Medium Term >3, < 10 years
Long Term > 10 years
Preferred Shares
Common Shares
3/ 79
Investment Management II - Investment Products 1
4Selected Investment Topics
Fixed Income Securities
Treasury Bills
Annuities
Zero-Coupon Bonds
Regular Bonds Review
Mutual Funds
Duration Concept
Cash & Cash Equivalents
4/ 79
5Cash & Cash Equivalents
Canada Savings Bonds
Treasury Bills
Deposits with Financial Institutions
GICs
Bank Accounts
Term Deposits
Special Features
5/ 79
6CDIC Insurance Coverage
Joe Savings + Checking + TD = 60,000
RRSP Fully Covered
Chapter 14, Problem 4
Joe Mary Jointly
Checking 5,000 1,000
Other 15,000 67,000 30,000
RRSP 35,000 90,000
Savings 40,000 5,000 10,000
GIC TDTD
GIC MF
www.cdic.ca.
6/ 79
Federal Budget, Feb 2005
Investment Management II - Investment Products 2
Maturity Days to
Maturity
Discount
Rates Asked
Change
Yield
Bid Asked
01-Aug-91 8 5.44 5.34 0.04 5.42
29-AUG-91 36 5.45 5.41 0.05 5.51
19-DEC-91 148 5.67 5.65 0.01 5.86
02-JUL-92 344 5.91 5.89 0.02 6.25
7CDIC Insurance Coverage
Mary Savings + Checking + GIC = 73,000
RRSP in MF Not Covered
Chapter 14, Problem 4
Joe Mary Jointly
Checking 5,000 1,000
Other 15,000 67,000 30,000
RRSP 35,000 90,000
Savings 40,000 5,000 10,000
GIC TDTD
GIC MF
www.cdic.ca.
7/ 79
Federal Budget, Feb 2005
8CDIC Insurance Coverage
Joint
Fully Insured Here
Each Joint Account Insured to 60,000
Chapter 14, Problem 4
Joe Mary Jointly
Checking 5,000 1,000
Other 15,000 67,000 30,000
RRSP 35,000 90,000
Savings 40,000 5,000 10,000
GIC TDTD
GIC MF
www.cdic.ca.
8/ 79
Federal Budget, Feb 2005
9Treasury Bills
Quoted as Bid/Ask Discount Rates
WSJ, July 23, 1991
9/ 79
Investment Management II - Investment Products 3
10Treasury Bills
BidSolve for P for 148 day Bill
discount rate = 360 ( 100 - P) N 100
x
5.67% = 360 ( 100 - P) 148 100
x
P = 97.669
Verify Seller is offering Bill for $97.677
10/ 79
11Treasury Bills
Bond Equivalent Yield
BEY = 365 ( 100 - P) N P
x
Bid BEY for 148 day Bill
BEY = 365 ( 100 - 97.669) 148 97.669
x
BEY = 5.89%
Verify Seller is offering Bill for BEY 5.86%
11/ 79
12Treasury Bills
US T-Bills maturing on Oct 12, 1995
were held for 2 weeks
Days
To Mat Discount Price BEY
30 99.554
44 99.357
1.Did rates rise or fall over the period?
2.Tax consequences on $10,000 FV?
5.26
5.35
5.36
5.45
BUY
SELL
12/ 79
Investment Management II - Investment Products 4
13Treasury Bills
Taxation
If Held to Maturity Interest
If Sold Before Maturity
Interest @ Original Yield
Remainder is Cap Gain/Loss
Fut Val = 9,935.70 x 1 + 0.0536 x 14
365
Simple Interest= 9,956.13
Interest = 9,956.13 - 9,935.70 = 20.43
Cap Gain= 9,955.40 - 9,956.13 = (0.73)
13/ 79
14Types of Orders
1.Market Immediacy
2.Limit
3. Stop-Loss
4. Stop-Buy
B.Time Specifications
1.Day
A.Price Specifications
2.Open or Good Till Canceled (GTC)
3.Good Through
14/ 79
15Types of Orders
1.All-or-None (AON)
C. Quantity Specifications
2. Any Part
3.Fill-or-Kill May be Time Based
D. How/What Specifications
1.Either-Or
2. Switch Order
3.Contingent Order
15/ 79
Investment Management II - Investment Products 5
16Types of Orders
1.Limit Stop Order
E. Special Limit Orders
• If price hit, does not become a market
order – sets a minimum price to be
achieved.
A Limit Stop Order to Stop at $23 with a
limit of $22 on the Stop Order
$22 Limit
$23
$25
Stop
16/ 79
17Types of Orders
2.Limit Order With Price Discretion
E. Special Limit Orders
Buy at $23 with “1/4 discretion”
• If can’t be bought at $23,
the trader can pay up to $23.25
F. Special Order Specifications
1. Cancel Former Order (CFO)
2. Delayed Delivery Order
3.Non-Client Order (NC or PRO)
17/ 79
18Accrued Interest
An investor sells 2 trading units of a
Government of Canada 12.5% bond
due December 15, 2014 on Tuesday,
June 13, 2000 at $116.
A. What is the accrued interest on this
transaction?
18/ 79
Investment Management II - Investment Products 6
19Normal Settlement for Stocks & Bonds
S M ST W Th F
Before
June 7, 1995
Same Day of Week
Settlement
S M ST W Th F
T+3 Settlement
T+5 Settlement
T+3 Business
= T+3 Calendar
S M ST W Th F
T+3 Business
= T+5 Calendar
19/ 79
20Accrued Interest
T+3 Business = T+(3 or 5) Calendar
Interest Earned
Per Day=
# Days
of Accrual x
Accrued
Interest
Jun 15 Dec 15Dec 15
Company Pays
Holder
Jun 13
Trade
Jun 16
Settlement
Settlement Period
20/ 79
21Accrued Interest
Interest Earned
Per Day=
# Days
of Accrual x
Accrued
Interest
Jun 16
Settlement
Jun 15 Dec 15
Company Pays
Holder
Jun 13
Trade
Dec 15
1 Day
Accrued
Interest = 1 Day x 12.5% x 2 x $100,000365 Days/yr = $68.49
21/ 79
Investment Management II - Investment Products 7
22Accrued Interest
An investor sells 2 trading units of a
Government of Canada 12.5% bond
due December 15, 2014 on Tuesday,
June 13, 2000 at $116.
A. What is the accrued interest on this
transaction?
B. How would your answer change if
instead the trade had taken place the
following day?
22/ 79
23Accrued Interest
19
Settlement
14 15
S M ST W Th F
June, 2000
16 17
18 20
Trade Coupon
Paid
# Days of Accrual = 4
23/ 79
24Trade Settlement of Stock
Transaction
Date
T T + 3
Settlement
Date
December, 1998
S M T W Th F S
1 2 3 4 5
20 21 22 23 24 26
27 29 30 3128
6 7 8 9 10 11 12
13 14 15 16 17 18 19
25
1. Last day to trade for settlement in 1998?
2. Ex-Dividend date if Record date 18th?
3. Record date if Ex-Rights date is 29th?
24/ 79
Investment Management II - Investment Products 8
8% Coupon
Bond
Market Interest Rates
7% 8% 9%
Maturity Price
%
Change Price Price
%
Change
1 year 100.94 0.94 100.00 99.08 (0.93)
5 years 104.10 4.10 100.00 96.11 (3.89)
10 years 107.02 7.02 100.00 93.58 (6.42)
20 years 110.59 10.59 100.00 90.87 (9.13)
4% Coupon
Bond
Market Interest Rates
7% 8% 9%
Maturity Price
%
Change Price Price
%
Change
1 year 97.20 0.94 96.30 95.41 (0.92)
5 years 87.70 4.37 84.03 80.55 (4.14)
10 years 78.93 7.89 73.16 67.91 (7.18)
20 years 68.22 12.33 60.73 54.36 (10.49)
25Regular Bonds
Rule 1: Inverse Rule
Rule 2: Maturity Effect
(Annual)
25/ 79
26Regular Bonds
Rule 3: Coupon Effect
Rule 4: Convexity
(Annual)
26/ 79
27Regular Bonds
Price
Interest Rates7 8 9
B
A
B > A
Convexity Property
27/ 79
Investment Management II - Investment Products 9
28Duration
Definition
Weighted Average Maturity
1 2 3 4 5
100
For 0%, 5 Year Bond Dur = Maturity
For 4%, 5 Year Bond
1 2 3 4 5
4 4 4 4 104
Portfolio of Zero Coupon Bonds
Dur < Maturity
28/ 79
29Macaulay Duration
For 4%, 5 Year Bond, Rates = 8%
Dur=
1 x 4
(1.08)1
2 x 4
(1.08)2
+
5 x 104
(1.08)5
++ ....
84.03
Bond Price= 4.59
Dur < Maturity
Calculation of Macaulay Duration
29/ 79
30Modified Duration
Calculation of Modified Duration
Modified Dur = Macaulay Duration
1 + K
For 4%, 5 Year Bond, Rates = 8%
Modified Dur = 4.59
1.08
= 4.25
30/ 79
Investment Management II - Investment Products 10
4% Coupon
Bond
Market Interest Rates
7% 8% 9%
Maturity Price
%
Change Price Price
%
Change
1 year 97.20 0.94 96.30 95.41 (0.92)
5 years 87.70 4.37 84.03 80.55 (4.14)
10 years 78.93 7.89 73.16 67.91 (7.18)
20 years 68.22 12.33 60.73 54.36 (10.49)
Coupon \Maturity 1 year 5 years 10 years 20 years
8% Duration 0.92 3.99 6.71 9.81
4% Duration 0.92 4.25 7.51 11.35
Coupon \Maturity 1 year 5 years 10 years 20 years
8% Duration 0.96 4.20 7.34 11.92
4% Duration 0.96 4.45 8.11 13.58
31Modified Duration
4.25Dur =
For 4%, 5 Year Bond, Rates = 8%
Approximate Change in Bond
Price If Rates Change By 1%
(Annual)
31/ 79
32Modified Duration
An Interest Rate Sensitivity Measure
At 8%
At 4%
32/ 79
33Duration
Longer DurationMore Volatile
Rule 2: Maturity Effect
Results: 1.Longer Maturity
2.Lower Coupon
3.Lower Rates
Rule 3: Coupon Effect
Rule 4: Convexity
33/ 79
Investment Management II - Investment Products 11
DUR PF
N
i 1
w i x DUR i
34Regular Bonds
Price
Interest Rates7 8 9
Convexity Property
Mod Dur = Tangent to
Curve
34/ 79
35Duration of Portfolio
Interest Rate Risks
Principal Risk
Reinvestment Risk
Duration of a Portfolio
i BAD
GOOD
If DUR = Planning Horizon,
Interest Rate Risk Can Be Eliminated
35/ 79
36Mutual Funds
Ownership in a professionally
managed portfolio of securities
A pool of funds from investors with
similar investment objectives
Indirect Ownership in a portfolio of
securities
36/ 79
Investment Management II - Investment Products 12
37
Closed-End Investment
Companies
Open End Funds
(Mutual Funds)
Mutual Funds
37/ 79
38Closed-End Investment Companies
Shares trade in secondary market
through brokers
Listed on Exchanges, or OTC
Like an ordinary company, but.....
Limited number of shares
Often trade at discount from
“portfolio value”
38/ 79
39Open-End Funds
Share or Unit Price Reflects
Proportionate Share of Portfolio
Unlimited Number of Shares
Units do not Trade
Purchase and Sale of Units Must be
Done Directly Through the Fund
Usually the “right to redemption”
39/ 79
Investment Management II - Investment Products 13
40
Fixed Income
Securities, T-Bills,
ST Gvt Bonds
Money Market
Funds
Interest
Income,
& Liquidity
Interest
Rate
Risk
Income or
Bond Funds
High Yielding
Govt & Corporate
Securities
Interest
Income
& Safety
of Principal
Interest
Rate
Risk
Mortgage
Funds Mortgages
Interest
Income
Interest
Rate
Risk !!
Dividend
Funds
High Quality Pref
Shares & Some
Common Shares,
From Taxable
Cdn Companies
Dividend
Income
Market
Risk
40/ 79
41
Balanced or
Diversified
Funds
Fixed Income
Securities,
Common
& Pref Shares
Income
& Capital
Appreciation
Interest
Rate &
Market
Risk
Growth or
Equity Funds
Common
Shares
Long Term
Capital
Appreciation
Market
Risk
Specialty
Funds
(Speculative)
Common Shares
of Companies
in one industry,
one geographic
location, or one
of the capital
market
Long Term
Capital
Appreciation
Market Risk
and the Risk
of an
Industry,
Commodity
or Region
41/ 79
42
International
or
Global Funds
Money Market,
Bonds or
Equities
Depends on
Securities
Held
Market
or Interest
Rate
& FX Risk
Real Estate
Funds Real Estate
Capital
Appreciaton,
income (?)
RE Market
&
Interest
Rate Risk
Ethical Funds Based on Moral Criteria
Capital
Appreciaton
Market
Risk
Index Funds Mirrors Specified
Index
Match Index
Returns
“Market”
Risk
42/ 79
Investment Management II - Investment Products 14
43
Segregated
Funds Various
Creditor
Proof
Insurance
Product
Portion of
Funds
Guaranteed
Limited
Market
Risk
www.bpifunds.com/english/legacy/le_fram.html
Labour
Sponsored
Venture
Capital
Corporations
(LSVCCs)
Common Shares
of small
businesses
Tax Credits
Long Term
Capital
Appreciation
Substantial
Risk,
Venture
Capital
Investments
43/ 79
44Advantages of Mutual Funds
Risk Reduction by Diversification
Professional Management
Many Investment Opportunities
Ease of Transfer in Fund Families
Automatic Reinvestment
Various Withdrawal Methods
Can Be Used as Collateral
44/ 79
45Weaknesses of Mutual Funds
Can’t Eliminate Market/Interest
Rate Risk
Some “Diversified” but “Specialized”
Not As Liquid as Common Stocks
(End of Day Trading)
Can’t Buy on Margin
Sales/Management Fees
Not CDIC Insured
Funds Can’t Put More than 10% of
Its Assets in One Company/Security45/ 79
Investment Management II - Investment Products 15
46Mutual Fund Fees & Charges
Front-End Loads
Load Funds
Back-End Loads
Based On Initial Investment
Based On Terminal Value
May Decline With Time
No Load Funds
46/ 79
47Mutual Fund Fees & Charges
• Management Fees
Average: 1.5% (0.25% to 2.8%)
• Higher fees with better performance
• Incentive Compensation
• Administrative & Custodial Fees
Average: 0.5% of MV total Assets
Average net monthly assets for year
Total Costs (except brokerage fees)=
Management Expense Ratio
Management & Other Fees
47/ 79
48Pricing of Mutual Funds
Offering (Buying Price)
No Load or Back-End Load
NAVPS
Front-End Load
Offering
Price =
NAVPS
1 - Load Charge(%)
NAVPS =
# of Shares O/S
MV Assets - Liabilities
Net Asset Value /Sh
48/ 79
Investment Management II - Investment Products 16
49Pricing of Mutual Funds
Selling Price
Back Load
NAVPS x [ 1 - Load Charge(%) ]
49/ 79
50Mutual Fund Pricing Example
Shares O/S 5 M
MV Securities $150 M
Liabilities $6.5 M
Shares Rec’d In Both Cases
With $1,000 Investment?
B) Back Load: 6%
Selling Price if A)No Load
Offering Price if A) No Load
B) Front Load: 5%
50/ 79
51Mutual Fund Pricing Example
No Load
NAVPS = $150 M - $6.5 M
5 M Sh
= $28.70/sh
Offering Price =Selling Price = $28.70/sh
Shares Rec’d = 34.8432
51/ 79
Investment Management II - Investment Products 17
52Mutual Fund Pricing Example
5% Front-End Load
Offering Price = $28.70
1 - 0.05
= $30.21/sh
Shares Rec’d = 33.1010
Selling Price = NAVPS
= $26.98/sh
6% Back-End Load
Selling Price = $28.70/sh x ( 1 - 0.06)
52/ 79
53Buying Mutual Funds
Accumulation Purchase Plans
Dollar Cost Averaging
Variable Ratio Plan
Constant Dollar Plan
Constant Ratio Plan
Lump Sum Purchases
Reinvesting Dividends
53/ 79
54Comparing MF Returns
Funds Must Have Same Investment
Objective
Time Frames Should Be Comparable
Performance Should Cover 1
Business Cycle
Funds Must Be Comparable
54/ 79
Investment Management II - Investment Products 18
55Risk vs Fund Objectives
82 64
Std Dev (%/mth)
3.80
5.90
4.57
Income
Balanced 3.05
2.67
3.93
Mean
Growth
Maximum
Capital Gain
Income-Growth
Growth-Income
Fund
Objectives
On average, the lower the
promised risk, the lower
the actual risk.
Some “conservative funds”
take on higher risk than
less conservative funds.
55/ 79
56MF Systematic Withdrawal Plans
Fixed Dollar Withdrawal Plans
Ratio Withdrawal Plans
Fixed Period Withdrawal Plans
Life Expectancy Adjusted
Withdrawal Plans
To Fund Educational Needs?
56/ 79
57MF Systematic Withdrawal Plans
To Meet Retirement Needs?
Fixed Dollar Withdrawal Plans
Ratio Withdrawal Plans
Fixed Period Withdrawal Plans
Life Expectancy Adjusted
Withdrawal Plans
57/ 79
Investment Management II - Investment Products 19
58MF Systematic Withdrawal Plans
To Leave an Estate?
Fixed Dollar Withdrawal Plans
Ratio Withdrawal Plans
Fixed Period Withdrawal Plans
Life Expectancy Adjusted
Withdrawal Plans
58/ 79
59Taxation of Mutual Funds
Taxation from 2 Sources
1. “Flow-Thru” of Interest, Dividends
& Capital Gains to Unitholder
2. Capital Gains (Losses) on
Redemption of Units
59/ 79
60Taxation of Mutual Funds
Taxation Depends on
2.How MF Is Structured
1.How MF Are Held
60/ 79
Investment Management II - Investment Products 20
61Taxation of Mutual Funds
How Held??
Outside RRSP
Inside RRSP
Taxed As
Income
When
Withdrawn
(1) Taxable On
Distribution
(2) CG Tax On
Sale
61/ 79
62Taxation of Mutual Funds
Fund Is
“Conduit” for
Unitholders
Distributes
Income &
“Flows Thru”
A Taxable Canadian
Corporation
How
Structured??
Corporation
Trust
62/ 79
63Mutual Fund Trusts
Investor
Mutual
Fund Investments
Government
Dividends
Interest
Gains
Flow-Thru
Reinvest?
63/ 79
Investment Management II - Investment Products 21
64Mutual Fund Corporations
Investor
Mutual
Fund Investments
Government
Dividends
Interest
Gains
No Tax
Cap Gains
Dividends
Reinvest?
64/ 79
65Effect of Cap Gains Distributions
Dec 21
NAV
30 Buy 50 Units
Action
Cap Gains
Dec 31 Distribution $10
Marginal Tax Rate 40%
20
$1,500
New Portfolio Value
Units 50 x $20 $1,000
Cash (CG) 50 x $10 500
Tax Payable ½ x $500 x 40% (100)
Portfolio Value $1,400
65/ 79
66Capital Gains On Redemption
Gain = NAV - ACB
ACB =
66/ 79
Investment Management II - Investment Products 22
67Capital Gains On Redemption
Jan 4 Buy 100 $15 4%
Units NAV FE-Load
Dec 311) $17
2)Interest Income $125
Apr 8 Sell 50 $21
ACB =
$15
(1 - 0.04 )
Purchase Price
No Load!!= $15.72/u
Gain = 50 u x ($21 - $15.72) = $264.00
67/ 79
68Calculations with Annuities
Annuity in Advance
1 2 30
100 100100
Ordinary Annuity
1 2 30
100 100100
68/ 79
69Annuity Products
Fixed Term• Immediate Annuity
Fixed Income• Deferred Annuity
• Term of Annuities
• Annuity Certain
• Life Annuity Guaranteed for N-Years
• Life Annuity
• Substandard Health Annuity
• Joint and Last Survivor Annuity
• Survivorship (or Reversionary) Annuity
# Registered (or Prescribed) Annuity
# Variable Annuity
69/ 79
Investment Management II - Investment Products 23
Annuities Page 1
Annuity Problems
1. Is an “Immediate Annuity” a regular annuity or an annuity in advance?
2 . George just purchased an annuity for $100,000. George will receive a monthly income
(starting next month) for 10 years. The insurance company is offering a nominal interest
rate of 8% compounded monthly.
A. What is the effective annual interest on this annuity?
B. How much will George receive each month from the annuity?
C. If the payment is to be made at the start of every period, how much will George receive
each month?
D. Why is the amount determined in C less than the amount determined in B?
E. Assume that 3 years have passed, and George dies. What is the capital remaining at that
time ?
F. How would your answer to B change if the insurance company was offering a nominal
interest rate of 9% compounded monthly? What conclusion can you draw from this?
3. Marty pays $200,000 for a deferred annuity which will begin to make monthly payments in
5 years, payable at the end of each month for a 10 year period. The insurance company
offers a nominal annual interest rate of 5.75% compounded monthly.
A. What will be the monthly amount that Marty will receive from this annuity?
B. How would your answer differ if compounding was to be done quarterly?
4. Melissa pays $200,000 for a deferred annuity which will begin to make monthly payments
in 5 years, payable at the end of each month. The insurance company offers a nominal
annual interest rate of 6.25% compounded monthly.
A. Melissa wants to receive $2,000 per month from the annuity. How long will she be able
to receive these payments for?
B. How is this payment option different from the one described in problem 4?
5. A woman in her 70s wants to receive a monthly check for the rest of her life. She puts
$100,000 in an immediate annuity and receives a check for $850 each month for the rest
of her life. About 65% of the payment is a return of her principle, so she pays taxes on
only 35% of the payment. If she lives to be 112, the checks keep coming. If she passes
away before the end of ten years, the monthly check can be paid to her heirs or her
favorite charity for the remainder of the ten years.
A. How would you describe this annuity, and how does it differ from the ones described in
Problems 3 and 4 above?
B. If the individual described above was a man instead of a woman, would the monthly
annuity payment be smaller, larger or the same? Explain.
Investment Management II - Investment Products 24
Annuities Page 2
6. Howard is now 70 years old and is expected to live another 4 years. He has purchased a
$100,000 variable annuity. The insurance company sets an Assumed Investment Return
(AIR) of 5% per year. Funds are invested in the TSE 300. Assume that over the course
of the next 4 years, the returns on the TSE are as follows:
1 2 3 4
6% 12% -9% 22%
A. Determine the amount of each annual payment that Howard will receive.
B. How much will the insurance company use to fund Howard’s benefits?
C. Does your answer in part A depend on i) the Assumed Investment Return (AIR) of the
insurance company? ii) the expected life of the annuitant? iii) the TSE 300 return?
Investment Management II - Investment Products 25
70 Deferred Annuity
Marty pays $200,000 for a deferred annuity which will
begin to make monthly payments in 5 years, payable at the
end of each month for a 10 year period. The insurance
company offers a nominal annual interest rate of 5.75%
compounded monthly.
A. What will be the monthly amount that Marty
will receive from this annuity?
200,000 x (1 + 0.0575/12) 60 = $266,435
Future Value in 5 years
266,435 = PMT x PVIFA(120 months, 0.0575/12)
PMT = $2,924.63
70/ 79
71Deferred Annuity ..
B. How would your answer differ if compounding
was to be done quarterly?
The Effective Annual Interest:
(1 + 0.0575/4) 4 -1 = 5.875%
The Effective Monthly Rate:
(1 + m) 12 = 1+0.05875 m = 0.4768%
The Future Value in 5 years
200,000 x (1 + 0.0575/4) 20 = $266,072
or 200,000 x (1 + 0.0004768) 60 = $266,072
266,072 = PMT x PVIFA(120 months, 0.4768%)
PMT = $2,916.88
71/ 79
72Registered or Prescribed Annuity
Capital Element
of each payment =
Capital Outlay
Total Payments to be Received
A 5-year annuity is purchased for $1,000.
Payments occur at the end of the year and
interest rates are 10% per annum.
Compare the interest actually earned to the
interest that is subject to tax.
Annual Payment $263.80
Capital Element $1,000
5 x $263.80
= = 0.75816
72/ 79
Investment Management II - Investment Products 26
10Rate5Time
1,000.00Outlay
0.7582Capital Element263.80Annual CF
TaxableEndAcccumulatedInterestStart
InterestValuePaymentValueEarnedValueYear
63.80836.20263.801,100.00100.001,000.000
63.80656.03263.80919.8283.62836.201
63.80457.83263.80721.6365.60656.032
63.80239.82263.80503.6145.78457.833
63.800.00263.80263.8023.98239.824
5
318.99318.99Total
73Registered or Prescribed Annuity...
73/ 79
74Variable Annuity
Howard is now 70 years old and is expected
to live another 4 years.
He has purchased a $100,000 variable
annuity. The insurance company sets an
Assumed Investment Return (AIR) of 5% per
year. Funds are invested in the TSE 300.
Assume that over the course of the next 4
years, the returns on the TSE are as follows:
1 2 3 4
6% 12% -9% 22%
74/ 79
75Variable Annuity.
Determine the amount of each annual payment
that Howard will receive.
The hypothetical constant payment is determined
by using the Assumed Investment Rate of 5%
p.a., and the expected life of the annuity – this is
set equal to the funds available.
100,000 = PMT x PVA(4 years, 5%)
PMT = 28,201
Investment Management II - Investment Products 27
100,000Starting Accumulation
5Assumed Investment Return
4Expected Life of Annuity
28,201Hypothetical Payment
EndAnnualActual
BalanceBenefitReturnTime
100,0000
77,53028,4700.061
56,46630,3680.122
25,06526,319-0.093
030,5800.224
76 Variable Annuity ...
The benefit payment in each year is given by the
recursive formula
Bt = B t-1 x 1 + R T
1 + AIR
The first year’s payment will be
28,201 x (1 + 0.06)/(1 + 0.05) = 28,469
The balance at the end of the year will be
= Prior Balance x (1 + RT) - Payment T
= 100,000 x (1+0.06) - 28,469 = 77,531
77 Variable Annuity ....
78Investor Protection
#
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Investment Management II - Investment Products 28
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Investment Management II - Investment Products 29
Formula Plans Page 1 of 6
Formula Plans A
Some of the following discussion is excerpted from Fundamentals of Investing, Lawrence Gitman andA
Michael Joehnk, Fifth edition, 1993.
Formula plans are mechanical methods employed by portfolio managers or investors to
try and take advantage of cyclical movements in security prices.
A) Dollar Cost Averaging
In this type of investment plan, a fixed dollar amount is invested in a security (or group
of securities) at regular fixed intervals, e.g., monthly..
Over time, the price of the security will fluctuate, so that when prices dip, more of the
security can be purchased with the fixed dollar amount, while at higher prices, less of the
security can be purchased. If prices are on average rising, the average cost of the
investment should be lower than the market value of the portfolio (Buy Low, Sell High).
The example on the following page illustrates how such a plan might operate over a single
quarter.
This investment plan is totally passive - no matter what the market conditions, the same
dollar amount is invested in the security each period.
Although a dollar cost averaging program could be applied to the acquisition of any
security, for it to eventually become successful requires that the security’s unit value must
eventually rise: it is therefore most appropriate with broadly based mutual funds. It would
also be useful to use with the HIPs or TIPs units described above.
Dollar Cost Averaging Example
Monthly Investment 200
Month NAV Month End Units Purchased
1 $23.00 8.696
2 24.00 8.333
3 19.00 10.526
4 25.00 8.000
Quarterly Summary
Total Investment $800.00
Total Units Purchased 35.555
Average Cost per Unit $22.50
Investment Management II - Investment Products 30
Formula Plans Page 2 of 6
Portfolio Value at End of Quarter $888.88
B) Constant Dollar Plan
In this and subsequent formula plans, there will be two parts to the investment portfolio:
one part is speculative, and the other is conservative.
In a Constant Dollar Plan, as the value of the speculative portion rises above a
certain amount or percentage, some of the speculative portion is sold off and these
funds are invested in the conservative portion of the portfolio (sell winners!). If the
speculative portion of the portfolio declines in value by a certain percentage or value,
some of the conservative portion of the portfolio is sold off and the funds re-invested in
the risky part (buy losers!).
The target dollar amount of the speculative portion is constant, with the investor deciding
on what price move is required to trigger a portfolio change.
In the example which follows, the portfolio initially consists of $20,000 divided equally
between a no-load mutual fund (speculative portion) and the remainder in a money market
fund (conservative portion). The investor has decided to rebalance the portfolio if the
speculative portion is worth $2,000 more or less than its initial value. This means that if
the value of the speculative portion exceeds $12,000, sufficient units of the mutual fund
are sold to bring its value back to $10,000. The proceeds from the sale of the mutual fund
are invested in the money market fund. If the value of the speculative portion falls below
$8,000, funds are transferred from the money market fund into the mutual fund.
Over the long run, if the speculative portion of the constant dollar plan rises in value, the
conservative component of the portfolio will increase in dollar value as profits are
transferred to it.
Constant Dollar Plan Example
NAV
Value of
Speculative
Portion
Value of
Conservative
Portion
Total
Portfolio
Value
Transactions Shares in
Speculative
Portion
10 10,000.00 10,000.00 20,000.00 1,000.00
11 11,000.00 10,000.00 21,000.00 1,000.00
12 12,000.00 10,000.00 22,000.00 1,000.00
L 12.00 10,000.00 12,000.00 22,000.00 Sell 166.67 sh 833.33
11 9,166.63 12,000.00 21,166.63 833.33
9.5 7,916.64 12,000.00 19,916.64 833.33
Investment Management II - Investment Products 31
Constant Dollar Plan Example
Formula Plans Page 3 of 6
L 9.50 10,000.00 9,916.64 19,916.64 Buy 219.30 sh 1,052.63
10 10,526.30 9,916.64 20,443.94 1,052.63
If no rebalancing had taken place (a simple buy and hold strategy), the final portfolio’s
value would have been $20,000, consisting of $10,000 in the speculative fund (1,000 units
x $10) and the $10,000 conservative portion.
C) Constant Ratio Plan
A Constant Ratio Plan is conceptually similar to the Constant Dollar Plan, except that a
fixed ratio of risky to conservative portions is maintained in the portfolio.
When the ratio exceeds a certain amount, rebalancing of the portfolio occurs, as
mentioned in the Constant Dollar Plan, to re-establish the desired ratio. The investor must
decide on the appropriate division in terms of speculative and conservative investments, as
well as the trigger points that result in rebalancing.
In the example which follows, the portfolio initially consists of $20,000 divided equally
between a no-load mutual fund (speculative portion) with the remainder in a money
market fund (conservative portion) -- the initial ratio of speculative to conservative being
1.00. The investor has decided to rebalance the portfolio if the speculative/conservative
ratio exceeds 1.20 or falls below 0.80. For example, when the NAV of the mutual fund is
$12, the ratio becomes 1.20, triggering the sale of 83.33 shares, which brings the portfolio
back to the 50:50 level.
Over the long run, if the speculative investment of the constant ratio plan rises in value,
the conservative component of the portfolio will increase in dollar value as profits are
transferred to it. This plan is therefore similar to the constant dollar plan, except that a
ratio is utilized as a trigger point.
Constant Ratio Plan Example
NAV
Value of
Speculative
Portion
Value of
Conservative
Portion
Total
Portfolio
Value
Speculative to
Conservative
Ratio
Transactions
Shares in
Speculative
Portion
10 10,000.00 10,000.00 20,000.00 1.000 1,000.00
11 11,000.00 10,000.00 21,000.00 1.100 1,000.00
12 12,000.00 10,000.00 22,000.00 1.200 1,000.00
L 12 11,000.00 11,000.00 22,000.00 1.000 Sell 83.33 sh 916.67
Investment Management II - Investment Products 32
Constant Ratio Plan Example
Formula Plans Page 4 of 6
11 10,083.00 11,000.00 21,083.00 0.917 916.67
10 9,166.70 11,000.00 20,166.70 0.833 916.67
9 8,250.00 11,000.00 19,250.00 0.750 916.67
L 9 9,625.00 9,625.00 19,250.00 1.000 Buy 152.78 sh 1,069.44
10 10,694.40 9,625.00 20,319.40 1.110 1,069.44
If no rebalancing had taken place the terminal value of the portfolio would simply remain
at $20,000.
D) Variable Ratio Plan
This is the most aggressive of the formula plans: again the portfolio is composed of
aggressive and conservative parts, but the ratio of these two parts change with market
conditions.
When the ratio of aggressive to conservative portion rises by a predetermined amount,
part of the aggressive portfolio is reduced; if the ratio declines below some trigger point,
the amount committed to the speculative portion is increased from the proceeds of the sale
of some of the conservative portion.
The decisions required are more complicated than in the other plans: the investor must
decide on the initial allocation between speculative and conservative portion of the
portfolio; the trigger points for buying and selling must be selected; and finally, the
adjustments in the ratio at each trigger point must be set.
This method attempts to time the cyclical movement in the mutual fund’s value: when the
fund moves up in value, profits are taken and the proportion invested in the lower risk
component is increased. When the speculative component’s value declines markedly, the
proportion committed to it increases.
In the example below, the portfolio is equally divided between speculative and
conservative portions. The investor has decided that when the speculative portion is 60%
of the total portfolio, its proportion will be reduced to 45%, while if the speculative
portion drops to 40% of the total portfolio, its proportion would be raised to 55%.
Variable Ratio Plan Example
NAV
Value of
Speculative
Portion
Value of
Conservative
Portion
Total
Portfolio
Value
Speculative to
Conservative
Ratio
Transactions
Shares in
Speculative
Portion
10 10,000.00 10,000.00 20,000.00 0.50 1,000
Investment Management II - Investment Products 33
Variable Ratio Plan Example
Formula Plans Page 5 of 6
15 15,000.00 10,000.00 25,000.00 0.60 1,000
L 15 11,250.00 13,750.00 25,000.00 0.45 Sell 250 sh 750
10 7,500.00 13,750.00 21,250.00 0.35 750
L 10 11,687.50 9,562.50 21,250.00 0.55 Buy 418.75 sh 1,169
12 14,025.00 9,562.50 23,587.50 0.41 1,169
Investment Management II - Investment Products 34