formula investing chapter 40 tools & techniques of investment planning copyright 2007, the...

Formula Investing Chapter 40Tools & Techniques of

Investment Planning

Copyright 2007, The National Underwriter Company 1

What is it?

• Formula investing is a strategy that seeks to limit the role of emotions in investing by adhering to a strict set of rules.

• Typically, formula investment strategies involve making fixed periodic investments through:– Dollar cost averaging, or– Dividend reinvestment plans.


Investment Planning


What is it?

• These two strategies can effectively lower the average cost of both equity and fixed-income securities in fluctuating markets.

• Other formula investing techniques are designed to minimize risk of interest rate fluctuations.– Bond laddering– Bond barbell strategies


Investment Planning


Dollar Cost Averaging

• Strategy: Make regular, periodic investments in a security without regard to price– It is a simple strategy practiced by many investors who may

not even realize it. – 401(k) investors who automatically invest a certain amount

each paycheck are practicing dollar cost averaging. – The premise behind dollar cost averaging is to take advantage

of market fluctuations to buy more shares when prices are low and fewer when prices are high.


Investment Planning


Example

• Let’s contrast an investment strategy where an investor purchases the same number of shares of a mutual fund each month with a dollar cost averaging strategy where an investor purchases the same dollar amount of a mutual fund each month.

• An investor has approximately $1,000 of discretionary income each month and would like to purchase shares of a mutual fund that is currently selling for $10 per share. Consider the following two strategies:– Strategy A - Purchase 100 shares per month; and– Strategy B - Purchase $1,000 per month.


Investment Planning


Dollar Cost Averaging – Variable PricesMonth Mutual

Fund Share Price

Strategy A – Shares

Purchased

Strategy A – Total Cost

Strategy B – Shares

Purchased

Strategy B – Total Cost

1 $10.00 100 $1,000.00 100.000 $1,000.00

2 $11.00 100 $1,100.00 90.909 $1,000.00

3 $11.00 100 $1,100.00 90.909 $1,000.00

4 $10.50 100 $1,050.00 95.238 $1,000.00

5 $10.00 100 $1,000.00 100.000 $1,000.00

6 $9.50 100 $ 950.00 105.263 $1,000.00

7 $9.00 100 $ 900.00 111.111 $1,000.00

8 $10.00 100 $1,000.00 100.000 $1,000.00

9 $11.00 100 $1,100.00 90.909 $1,000.00

10 $12.00 100 $1,200.00 83.333 $1,000.00

11 $12.00 100 $1,200.00 83.333 $1,000.00

12 $11.00 100 $1,100.00 90.909 $1,000.00

Total 1,200 $12,700 1,141.914 $12,000


Investment Planning


Example

• Strategy A– The investor has 1,200 shares at the end of the year with an

average cost of $10.583.– The value of the 1,200 shares is $13,200.00 at the final price

of $11.00/share, and there is an unrealized gain of $500.00

• Strategy B– The investor has 1,141.914 shares with an average cost of

$10.509– The value of the shares is $12,561.05 and there is an

unrealized gain of $561.05


Investment Planning


Example

• By purchasing more shares when the price is low and fewer shares when the price is high, the investor lowered his average cost basis with Strategy B.

• Consequently, the investor finished with greater investment gains (as measured by the unrealized gains of $561.05 vs. $500.00) on the amounts actually invested.

• The investor maintained a predictable investment outlay.– He was not struck with the need to find additional funds for

investment in months when the share price was higher.


Investment Planning


Dollar Cost Averaging – Increasing Prices

Month Mutual Fund Share Price

Strategy A – Shares

Purchased

Strategy A – Total Cost

Strategy B – Shares

Purchased

Strategy B – Total Cost

1 $10.00 100 $1,000.00 100 $1,000.00

2 $10.10 100 $1,010.00 99.01 $1,000.00

3 $10.20 100 $1,020.00 98.039 $1,000.00

4 $10.30 100 $1,030.00 97.087 $1,000.00

5 $10.40 100 $1,040.00 96.154 $1,000.00

6 $10.50 100 $1,050.00 95.238 $1,000.00

7 $10.60 100 $1,060.00 94.34 $1,000.00

8 $10.70 100 $1,070.00 93.458 $1,000.00

9 $10.80 100 $1,080.00 92.593 $1,000.00

10 $10.90 100 $1,090.00 91.743 $1,000.00

11 $11.00 100 $1,100.00 90.909 $1,000.00

12 $11.10 100 $1,110.00 90.09 $1,000.00

Total 1,200 $12,660 1,138.66 $12,000


Investment Planning


Example

• Strategy A– Average cost of $10.55– Value of $13,320– An unrealized gain of $660.

• Strategy B– Average cost of $10.54– Value of $12.639.14– An unrealized gain of $639.14

• Note that the dollar cost averaging (Strategy B) resulted in the lower average cost, but not the maximum gain in this case.


Investment Planning


Lump Sum versus Dollar Cost Averaging

• Let’s assume that Andrea, a 30-year old with limited investments, earns a $12,000 bonus received at the end of January.

• She has a choice of investing the entire amount in an S&P 500 index fund at one time or spreading the investment evenly over the next 12 months.

• Each share in the fund currently sells for $9.12. • If she invests the entire lump sum at once, she can

purchase just over 1,315.8 shares. • She is not sure whether the market will rise or fall over the

next 12 months and decides to spread the investment over the course of the year.


Investment Planning


Lump Sum versus Dollar Cost Averaging

• To the right are the month-end values for the fund purchases Andrea makes.

• At the end of the year, she has about 1,344 shares.– 28 more shares than she would have purchased had

she bought them all up front.• At the final price of $9.75/share, her investment has

grown to $13,103 instead of $12,829.– An additional $274.

• The reason is that, as the market fell early in the year, she was able to buy a larger number of shares each month (at a lower cost).

• Because she was able to take advantage of market fluctuations, she ended the year with more than 2% of additional value than she would have had by investing as a lump sum up-front.

Month Fund Shares

January $9.12 109.6

February $9.16 109.2

March $8.15 122.7

April $8.86 112.9

May $9.36 106.8

June $8.80 113.6

July $8.56 116.8

August $8.41 118.9

September $8.48 117.9

October $9.16 109.2

November $9.64 103.7

December $9.75 102.6

Total 1,343.9


Investment Planning



• Dollar cost averaging works best when markets are declining or fluctuating.– The investor is able to buy more shares when prices fall (and

purchases fewer shares when prices are higher). – In this sense, it is a contrarian strategy.

• Dollar cost averaging does not work in a steadily rising market.– The investor would be better off buying as much as possible at

the lower initial price than to pay more each month for a smaller number of shares.


Investment Planning



• Referring to our previous example, since markets do tend to rise over the long term, it would usually not make sense for Andrea to spread her investment over years rather than months.– Even though Andrea has a long time horizon and should buy as

much in the early years as possible, she must currently make a decision about investing a specific amount of available cash.

– By spreading the investment over 12 months, she is able to benefit from market fluctuations (since the market did occasionally decline) and at least ensure that she does not (accidentally) invest all of her money at a market peak.

– It also allows her to establish an investing discipline.


Investment Planning


Market Peaks and Dollar Cost Averaging

• The consequences of investing at a market peak instead of dollar cost averaging can be quite substantial.

• Assume the returns from the prior example involving Andrea occurred in reverse order, such that the market started at 975 and finished at 912.

– The results of this scenario are in the table on the right.

• At the end of the year, Andrea still has about 1,344 shares through a dollar cost averaging program, worth $12,256.

• If Andrea had made a lump-sum investment of her $12,000, she would have only been able to purchase about 1,231 shares at the high price of $9.75/share.

– At the end of the term, this would have only been worth $11,225

Month Fund Shares

January $9.75 102.6

February $9.64 103.7

March $9.16 109.2

April $8.48 117.9

May $8.41 118.9

June $8.56 116.8

July $8.80 113.6

August $9.36 106.8

September $8.86 112.9

October $8.15 122.7

November $9.16 109.2

December $9.12 109.6

Total 1,343.9


Investment Planning



• For many investors, dollar cost averaging is as much a matter of necessity as of choice.

• For those that do not have a lump sum available to invest, dollar cost averaging becomes the de facto strategy.– They make purchases as cash becomes available to invest.


Investment Planning


Dividend Reinvestment

• Dividend reinvestment plans (DRIPs) allow shareholders to take dividends in the form of additional shares rather than cash. – Many companies with dividend reinvestment plans allow

shareholders to purchase shares commission-free (or with a minimal transaction fee) through their dividend reinvestment plan

– Other companies offer shareholders discounted share prices in return for reinvesting dividends.


Investment Planning


Dividend Reinvestment

• At their simplest, dividend reinvestment plans are a form of dollar cost averaging. – Instead of accepting a cash dividend, the dividend is

reinvested at the then-prevailing price.

• The most basic advantage relates to cash planning.– By reducing costly transaction fees and commissions, the

investor is able to put more of his investment dollars to work

over the long run and earn more.


Investment Planning


Fixed Income Strategies

• Just as with equity investments, bonds are subject to risk. – Bond investors share the desire to maximize their return for a given

level of risk.

• For risk averse investors there are ways to reduce the risk of investing in bonds.– An investor who does not want to face any default risk could limit

investments to U.S. government bonds.

– If a somewhat greater return is sought, investing in a diversified portfolio of corporate bonds might be appropriate.

• Diversification reduces the negative impact of any single bond defaulting by reducing the amount invested in any particular bond.

– Various strategies such as immunization can also help reduce risk when investing in individual bonds.


Investment Planning



• As with any investment, bond investments can be actively managed or left alone.

• Passive approach– Such an approach usually entails selecting a portfolio of bonds to

match an investor’s preferences toward factors such as time horizon, tax status, and risk, and simply holding them until maturity.

– Basic Assumption: Markets are relatively efficient. Superior returns cannot be obtained by timing the market or continuously looking for mispriced assets.

– As with all investments, individual assets and the portfolio as a whole should be examined for appropriateness.

– Techniques such as immunization and laddering can be used to reduce portfolio risk over time.


Investment Planning



• Active Approach– Basic Assumption: Markets are less than efficient. Superior (to the

passive approach) returns can be generated through market timing and asset selection.

– Active management can involve analyzing particular bonds and sectors or forecasting anything from interest rates to inflation to economic outlook – looking for mispriced securities and seeking to avoid areas that (in the investor’s opinion) may decline in value.

• This will usually result in more active trading or swapping of bonds within the portfolio.

• It may require substantial additional investments of time for research and analysis.

• Passive and active strategies are not always mutually exclusive.– Some techniques have elements of both and can be useful to all investors.


Investment Planning


Immunization

• Immunization involves selecting a bond or portfolio of bonds such that interest rate movements result in bond price fluctuations (interest rate risk) and cash flows for reinvestment (reinvestment risk) that offset one another. – These two risks move in opposite directions.– If interest rates rise, interest rate risk causes the value of our

bond to drop, but we earn more on any coupon payments that are reinvested.

– On the other hand, if rates decline, the value of our bond rises, but we earn less from reinvestment.


Investment Planning


Immunization

• Macaulay duration measures the point in time when these two risks precisely offset each other.– By matching the duration of our bond to our investment horizon

we can offset interest rate and reinvestment risk. – If we purchase a bond and sell it when it reaches its duration

(as calculated upon purchase), any loss in bond value caused by an increase in interest rates should be offset by the increase in the reinvestment earnings of interest payments.

– If interest rates decline, the loss in reinvested earnings should be offset by an increase in the value of the bonds.


Investment Planning


Immunization

• Immunization can be accomplished easily using zero coupon bonds.– Their maturity is their duration. – No computations are necessary. – There is no reinvestment risk related to interest payments,

since there are no interest payments.


Investment Planning


Ladder Portfolio

• Reinvestment risk also occurs when bonds mature earlier than the investor needs the proceeds– Although a strategy of purchasing very long-term bonds to

secure a long-term expected return can mitigate reinvestment risk, substantial danger exists in this strategy because long-term bonds are more sensitive to changes in interest rates than shorter-term bonds.

– If it turns out that the investor must use the money for an emergency or chooses to retire early, the investor may be stuck at an inopportune time with depressed bond prices in the face of a rising interest rate environment.


Investment Planning


Ladder Portfolio

• A laddered portfolio can help mitigate reinvestment risk.

• In a laddered portfolio, you invest in an assortment of bonds with staggered maturities.


Investment Planning


Ladder Portfolio

• Example: Structure a portfolio where 10% of the bonds mature each year. – The bonds would not all mature in the same interest rate

environment.– Environment in which interest rates are rising

• The value of the portfolio may fall, but the investor does not need to sell bonds that haven’t matured.

• If cash is needed, the maturing bonds offer a ready source. • If cash is not needed, the investor can reinvest the proceeds of

the maturing bonds at the new (higher) interest rate. – Environment in which interest rates are falling

• The investor will reinvest the proceeds at a lower rate, but only for 10% of the portfolio.

• The longer maturity bonds would rise in value.


Investment Planning


Ladder Portfolio

• With a laddered portfolio, the proceeds of maturing bonds would be reinvested in new bonds with a maturity later than those currently in the portfolio.

• A bond ladder reduces interest rate risk by staggering maturities among several bonds.– For a long-term investor, this ends up being similar to a dollar

cost averaging strategy.– Shorter maturities cushion interest rate risks, while the fact

that only a portion of the bonds mature in a given period reduces reinvestment risk.

• If rates should rise, the maturing bonds can be used to buy bonds offering a higher yield.


Investment Planning


Ladder Portfolio

• A bond ladder also enables the investor to match cash flows with planned expenditures.– Example: A retired investor can plan a laddered bond portfolio

to include regularly maturing bonds that provide the cash necessary for annual living expenses.

• Bond ladders also work for unplanned expenses.– Example: If the investor loses his job, maturing bonds can be

used to supplement lost income.


Investment Planning


Ladder Portfolio

Maturity Yield Amount Invested

Purpose

3 month 1.0% $10,000 Emergency fund

2 year 1.8% $10,000 Hedge against rising rates

3 year 2.3% $10,000 Higher yield hedge

5 year 3.3% $10,000 Yield

10 year 4.4% $10,000 Yield

15 year 4.5% $20,000 Planned tuition payment




20 year 4.8% $10,000 Yield

25 year 5.0% 20,000 Yield, hedge against falling rates

30 year 5.2% 30,000 Yield, retirement and hedge against falling rates


Investment Planning


Barbell Strategy

• A barbell strategy offers another means of balancing the risks in a bond portfolio.

• The barbell places heavy weights on very long and very short maturities, with no position in intermediate-term securities.– Advantage: It can be established with fewer bonds, reducing

complexity and transaction costs.• Only long and short maturities are required.

– Disadvantage: The investor may be unable to match maturities

with cash needs as effectively.


Investment Planning


Barbell Strategy

• A barbell allows the investor to create a fairly effective hedge against both interest rate and reinvestment risk, simply and at low cost. – If rates go up, the short portion of the barbell can be

reinvested at the higher rate and help offset losses in the longer maturity.

– If rates decline, the long maturity gains make up for the lower interest rate available for reinvestment of the short maturity portion.


Investment Planning


Barbell Portfolio

Maturity YieldAmount Invested

Purpose

3 month 1.0% $50,000Emergency fund and hedge against rising

rates

30 year 5.2% $50,000Long-term needs and

profit from falling rates


Investment Planning


Barbell Strategy

• A barbell strategy can also be appropriate based upon the current shape of the yield curve and expected changes in interest rates.

• It can also result in a portfolio with the same duration as a bullet strategy (a single bond maturity), but with higher convexity. – Convexity measures the curvature of the relationship between

bond yields and prices. • Positive convexity is always a good thing for the bond investor,

regardless of whether interest rates rise or fall. – If interest rates fall, then convexity will augment the rise in the

price of the bond. – If interest rates rise, convexity will dampen the decline in price.


Investment Planning


Where Can I Find Out More About It?

1. Frank J. Fabozzi, Ed., The Handbook of Fixed-Income Securities, 6th Edition (New York, NY: McGraw Hill, 2000)

2. Annette Thau, The Bond Book, 2nd Edition (New York, NY: McGraw Hill, 2001)

3. Marilyn Cohen and Nick Watson, The Bond Bible (New York, NY: New York Institute of Finance, 2000).

formula investing chapter 40 tools & techniques of investment planning copyright 2007, the...

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