### Introduction

It's a scary time for equity investors. Recent experience provides a reminder of just how volatile stock markets really are. While investors enjoy the "good" volatility that occurs when stocks rise, they do not like to experience the "bad" volatility that occurs when stocks fall.

Investors want stock market insurance. Every insurance policy has a cost. We need to look at the risk we want to insure, and we need to look at the cost of the insurance.

### Stock Market Risk

Figure 1 shows the downside risk for Canadian investors. The data shown in this Figure covers 79 years of stock market history since the inception of the Toronto Stock Exchange. It includes the Great Depression and World War II.

Figure 1

Probability of Under-Performance

Canadian Stock Market Returns 1919 - 1997

Total Return (Capital Appreciation plus Reinvested Dividends)

This figure shows the probability P that a Canadian stock market investment held for n years will have an annual compound return below that shown on the y-axis. For example, there is a probability of 0.159 (1 chance in 6) that the Canadian stock market will lose more than 10% in any single 12 month period.

Over the 79 years in which the Toronto Stock Exchange has existed, the mean return has been a little over 9% annually for all holding periods. This is shown as the "P=0.5" line in Figure 1. There is a 50% probability of doing better than 9% from an investment in stocks, and a 50% probability of getting less than a 9% annual return, no matter how long you hold your investment.

A 9% return sounds very meager compared to stock market performance over the past three years. It is, however, consistent with long term performance. For example, Canada's oldest mutual fund, the Canadian Investment Fund, has had a 9.1% compound annual return since its inception in 1932. Recent stock market performance has been exceptionally high. It is not reasonable to expect high returns to continue into the future.

The other lines on the graph show other return probabilities. If you have a 5 year time horizon, over those 5 years you have a 50% probability of getting better than a 9% return, but also a 15.9% probability (P=0.159; roughly 1 chance in 6) of just breaking even. There is also 1 chance in 1000 (P=0.001) that you could lose money at the rate of 14.6% per year over the 5 years! Suppose Suzie invested $1,000. She has a 50% probability of having $1,539 or more at the end of 5 years (and the same probability of having less than $1,539). She also has a 15.9% probability of having less than $1,039 after 5 years, and 1 chance in a 1000 that her investment could dwindle to only $454 after 5 years had passed!

The worst performance actually achieved by the Toronto Stock Exchange during the 79 years of its existence occurred during holding periods which all began in 1929 or 1930. These were all worse than the "1-in-1000" returns shown in Figure 1. Table 1 indicates the worst performance of the TSE total return index in the modern era, since 1956. It is possible to obtain poor investment returns from stock market investments over substantial periods of time! As another example, consider that the Dow Jones Industrial Average first hit the 1000 level in 1965. It was only in 1982 — 17 years later — that it passed that level for (hopefully) the final time. How many current stock market investors are willing to hold onto an investment for 17 years without getting any return whatsoever?

Table 1

Worst Performance of the Toronto Stock Exchange

Total Return Index 1956 - 1997

Holding Period | Holding Period | Annual Compound Return |

1 Year | June 1981 - June 1982 | -37.73% |

2 Years | July 1980 - July 1982 | -16.29% |

3 Years | Oct 1973 - Oct 1976 | -4.85% |

5 Years | Dec 1969 - Dec 1974 | -0.61% |

10 Years | Dec 1964 - Dec 1974 | +3.21% |

20 Years | May 1957 - May 1977 | +6.08% |

It is apparent from Figure 1 that the downside risk from holding equities is reduced as the holding period increases. Those who claim that a portfolio of stocks always outperforms a portfolio of fixed income investments "over the long term" are not telling the full story!

Given this market risk profile, you may decide that you don't need stock market insurance after all. Alternatively, you may decide that the probable future return is not worth the uncertainty, and that you'll avoid the stock market completely. Both are perfectly rational decisions.

You may also decide that your head likes the potential returns from the stock market, but your stomach finds the bumps a little too hard to withstand. You need some stock market insurance. This insurance is available in many forms.

### Equity-Linked GICs

Banks and trust companies offer equity-linked GICs. They are most suitable for those with less than $10,000 inside an RRSP. These securities are not suitable for anyone investing outside an RRSP because the tax treatment is unfavourable.

Equity-linked GICs are very sophisticated securities, but may be sold in banks by staff who do not hold a securities licence. There are major differences between the products sold by different financial institutions; it is essential to shop around. The GICs can be linked to Canadian stock market performance (TSE35, TSE100 or TSE300 indexes), or to a basket of G7 international indexes. All are Canadian content for RRSP purposes.

In most cases it is difficult to determine the cost of the market insurance. Do not expect much help from bank staff. Here are some of the possible costs:

- Minimum return is generally return of capital without interest; a regular GIC pays an assured rate of interest. Cannot be sold prior to maturity.
- Return is linked to the return of the underlying index, excluding dividends. Dividends play a major role in total equity returns. Since 1954, the TSE300 index has returned 10.0% annually with dividends included, but only 5.6% without dividends.
- There may be a maximum allowable return. This could be a specific cap, or there may be incomplete participation in the rise of the underlying index (for example, 60% of the rise of the underlying index).
- The final value may be based on the average of the underlying index over the final year, not the value of the index at maturity. This is good if markets fall in the final year, but not if they rise that last year.
- There is limited ability to switch or lock in profits.

Suppose your bank is selling a 5-year TSE300 equity-linked GIC with a 60% market participation rate. Suppose also that the TSE performs at its average of 5.6% annually without dividends. The return from the GIC would be 60% of 5.6%, or only 3.3% annually. A regular 5-year GIC yields around 5.25% annually. Which would you prefer?

### Do-It-Yourself GICs

It is possible to be just like the banks, and make your own equity-linked GIC. You can do it yourself, at much lower cost. You'll need an account at a brokerage. The firm's KYC (personal information sheet) should say that you are an experienced and informed investor.

There are two ways to build your own equity-linked GIC:

- Buy a strip bond with a portion of your investment, and purchase a long-dated call option on the index of your choice with the remainder.
- Buy TIPs, HIPs, S&P Depository Receipts (SPDR) or an equity mutual fund with a portion of your money, and purchase a long-dated put option at the money to protect the downside risk.

If you do not understand what these strategies mean, you do not understand what the nice person at the bank is actually selling you. Perhaps you should not be buying what you do not understand.

Like equity-linked GICs, these strategies will yield the index return without reinvested dividends on the upside, but without any market cap. They will provide for the return of initial capital, without interest, on the downside.

### Segregated Funds

Life insurance companies offer segregated funds. These are technically insurance products, but can be considered as mutual funds with a money-back guarantee. They may be suitable for any investor, but are particularly suited to self-employed business people who want to creditor-proof their RRSP. They also have application for estate-planning purposes.

Unlike equity-linked GICs, equity segregated funds use a total return index as their benchmark. You can easily sell or switch segregated funds, just like regular mutual funds.

Segregated funds used to have a much higher management expense ratio (MER) than their mutual fund cousins, but the spread has narrowed in recent years. For example, the C.I. Segregated Harbour Fund has an MER only 0.4% higher than the C.I. Harbour Fund. This difference ($4 per $1000 invested) is the cost of the stock market insurance.

### Strip Bond + Equity Investment

Strip bonds have unfavourable tax treatment, so this approach is most appropriate inside an RRSP. You need enough money in the RRSP to make a self-directed plan worthwhile (more than $10,000).

Suppose you have $10,000 to invest. With this approach, you would purchase a strip bond with the maturity desired with a portion of the money. For example, a 5-year Government of Canada strip bond worth $10,000 at maturity may cost $7,651 today. You would place the remaining $2,349 in an equity mutual fund.

At maturity, the value of the investment is $10,000 plus whatever the value of the mutual fund happens to be. As a minimum, this combination will be worth more than the return from an equity-linked GIC. This is true unless the value of the mutual fund falls to zero, which is not possible without a total collapse of Western civilization.

Two factors affect the upside potential of this strategy: the return from the equity mutual fund, and the ratio between the initial cost of the mutual fund and the total investment. The ratio is equivalent to the "market participation rate" of the equity-linked GIC. It works best for those with a time frame longer than 5 years, so the mutual fund represents more than half of the initial investment.

### Balanced Funds

Balanced funds are not generally thought of as an "insurance" policy, but their returns have historically been much more stable than the returns from equity investments. Balanced funds are appropriate both within and outside an RRSP. They are also suitable for those without sufficient funds to justify a self-directed RRSP.

Recent advertising has emphasized the returns from balanced funds. I find this a scary notion. We have not had a bear market in equities or bonds for over five years. The performance numbers being advertised do not represent long term performance. It is a market reality that the best performers in good times will be the worst performers in bad.

I prefer to look at risk exposure when evaluating balanced fund managers. I look particularly at 1990, when only 38% of Canadian balanced fund managers had positive returns. There is one Canadian balanced fund manager (Larry Kennedy, manager of the Guardian Canadian Balanced Fund) who has not had a negative year since 1981, and whose 10 year returns are very competitive.

It is also possible to create your own balanced fund through the purchase of equity and bond mutual funds. The equity portion is for growth; I look for strong performance there. The bond portion is for stability. I consider high 3-year returns a negative feature. I look particularly at 1994, when only one Canadian bond fund (Dynamic Income Fund) had positive returns. That's the kind of performance I want from my fixed income manager.

There are two additional costs when evaluating balanced funds versus the strip bond plus equity approach:

- The fixed income portion of the balanced fund has a substantial management fee, versus no management fee for a bond held in a self-directed RRSP.
- The fixed income portion of a balanced fund never matures. It is possible to permanently lose capital on the fixed income portion of a balanced fund. This cannot happen with a strip bond held to maturity.

### Portfolio Optimization

Portfolio optimization is a more sophisticated approach to building a balanced portfolio than either the balanced fund approach or the strip bond plus equity approach. Portfolio optimization is based upon Modern Portfolio Theory, which won the Nobel Prize for its developers. The method starts with the premise that the total return from a portfolio is more important than the returns from any component within the portfolio. The technique uses the expected returns and variability characteristics of a variety of potential investments, and the correlations between the returns. It mathematically computes a portfolio that will produce the best possible return with the least possible uncertainty of that return.

Several financial institutions offer portfolio optimization services. The best is probably the Mackenzie STAR programme. These services use a questionnaire to estimate the customer's risk tolerance, then aim to get the best possible return within that constraint. These services do not quantify upside potential nor downside risk.

The best optimization services quantify tolerance for downside risk and targeted return. For example: would you be willing to accept the possibility of having your portfolio drop 5% in value in any year, in exchange for being 95% confident of receiving an 11% average return over the next 5 years? These services show the trade-off between risk and reward to the client. Portfolio optimization is a distinct improvement over a straight balanced fund approach.

### Conclusions

There are many ways by which an investor can protect against stock market volatility. Each has its own advantages and disadvantages. They range in simplicity from the straight balanced fund to derivative-based products like equity-linked GICs and to the mathematics of portfolio optimization.

Insurance against market volatility has a cost. It is often difficult, and sometimes impossible, to determine the cost of any stock market insurance program.