PWL Capital recently released its latest Financial Planning Assumptions for market-cap weighted portfolios document.[1] These are projections for asset class expected mean returns, standard deviations, and correlations covering stocks, bonds, and the primary residence. We additionally calculate expected returns and standard deviations for portfolios of stocks and bonds at various proportions. These projections cover a 30-year horizon and are based on the premise that the investor holds a broadly diversified portfolio of Canadian bonds and global equities.
In our experience, long-term expected inflation is perhaps the most challenging variable to assess using statistical methods in financial markets. We rely on a simple average between the following three factors:
1. The breakeven point between Canadian long-term fixed-rate bonds and real return bonds (currently 2.1%)
2. The Bank of Canada inflation target rate (currently 2.0%)
3. The historical rate of inflation in Canada since the year 1900 (currently 3.0%)
With this methodology we obtain a projected inflation rate of 2.4%, which serves as the foundation for calculating nominal asset class expected returns.
The primary residence constitutes a significant portion of wealth for most retail investors. Shiller (2006) estimates the real appreciation rate of long-term residences between 0.2% and 0.4% per year, while Jorda (2017) estimates it at 1.1%. We opt for a projected real rate of appreciation of 1%, from which we must deduct property taxes, insurance, and maintenance costs. We suggest removing 1% for maintenance and insurance, while property taxes are so different from place to place that they must be assessed on a case-by-case basis. It is worth mentioning that the appreciation rate of the residence is not a complete estimate of its expected return because it does not consider either the rent that is saved by acquiring a home or the cost of opportunity on the capital invested in the property.
The volatility of the Canadian real estate market since 1992 is 3.5%, but this does not consider each house’s specific risk. To assess this specific risk, we base ourselves on the studies of Haurin and Zhou (2010) and Peng and Thibodeau (2016), who estimate the average specific volatility of individual residences in the United States at 10.6%. By adding the market risk and the specific risk, we arrive at an annual volatility of 14.1% for residential properties in Canada, a figure similar in magnitude to stock market indexes.
We calculate the expected returns of asset classes based on both their historical returns since 1900 and specific market signals including Canadian bond yields and the respective stock markets’ price/earnings ratios adjusted for market cycles. These returns are nominal, i.e., they include inflation at our previously mentioned estimate. Our estimates also account for investment product fees. To do this, we deduct the management expense ratios of low-cost ETFs corresponding to each asset class. Details are shown in Table 1.
Table 1 –Asset class Expected Returns
| Asset Class | Gross Expected Return | Representative ETF | MER | Net Expected Return |
| Canadian Bonds | 4.25 % | Vanguard Aggregate Bond | 0.09 % | 4.15 % |
| Canadian Stocks | 7.00 % | iShares S&P/TSX Composite | 0.05% | 6.95 % |
| US Stocks | 6.72 % | Vanguard US Total Market | 0.15 % | 6.56 % |
| International stocks | 7.66 % | Vanguard FTSE All Cap Ex North America (70%) et Vanguard FTSE Emerging Market All Cap (30%) | 0.23 % | 7.41 % |
Source: PWL Capital; Data sources: Bloomberg, Morningstar, Robert Shiller, Elroy Dimson, Paul Marsh and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press, 2002; Elroy Dimson, Paul Marsh and Mike Staunton, Credit Suisse Global Returns Yearbook and Sourcebook, 2018, Zurich: Credit Suisse Research Institute, 2021
Standard deviation is a measure of the risk of an asset class. Theoretically, a rational investor seeks a portfolio with the lowest possible volatility for a given level of expected return. We estimate the expected standard deviation using an average of the standard deviations over 5 and 20 years. According to Table 2 below, stocks have about three times the risk of bonds. An estimate for standard deviation is important when running probability simulations such as Monte Carlo to test financial planning scenarios.
Table 2: Standard deviations of asset class returns
| Asset Class | Standard Deviation |
| Canadian Bonds | 4.96 % |
| Canadian Stocks | 15.50 % |
| US Stocks | 14.99 % |
| International stocks | 13.12 % |
Source: PWL Capital; Data sources: Morningstar
Correlation indicates how much the asset classes fluctuate in concert with each other. A correlation of 1 indicates perfect synchronism, while a correlation of -1 indicates perfect reverse synchronism. A correlation of zero indicates that the variables fluctuate independently. Theoretically, a rational investor should look for asset classes with the least possible correlation to reduce the whole portfolio’s standard deviation. As shown in Table 3, the correlation between bonds and stocks is relatively low, while that between the various stock markets is rather high.
Table 3: Correlation of asset classes
| Fixed Income | Canadian Equity | U.S. Equity | International Equity | |
| Fixed Income | 1.00 | 0.27 | 0.35 | 0.34 |
| Canadian Equity | 0.27 | 1.00 | 0.73 | 0.73 |
| U.S. Equity | 0.35 | 0.73 | 1.00 | 0.77 |
| International Equity | 0.34 | 0.73 | 0.77 | 1.00 |
Source: PWL Capital; Data sources: Morningstar
Our estimates of expected returns are among the highest we have produced in recent years, mainly thanks to the rise in bond yields. Table 4 provides a comparison of expected returns for different asset allocations. A classic portfolio weighted 60% in stocks, and 40% in bonds sees its expected return increase by 0.84% compared to last year.
Table 4 – Expected Portfolio Returns (before fees)
| Asset allocation | Expected Return 2022 | Expected Return 2023 | Difference |
| 0% Global Stocks / 100% Bonds | 2.48 % | 4.15 % | + 1.67 % |
| 40% Global Stocks / 60% Bonds | 4.11 % | 5.26 % | + 1.15 % |
| 60% Global Stocks / 40% Bonds | 4.97 % | 5.81 % | + 0.84 % |
| 80% Global Stocks / 20% Bonds | 5.78 % | 6.36% | + 0.58 % |
| 100% Global Stocks / 0% Bonds | 6.62% | 6.91 % | + 0.29% |
Source: PWL Capital; Data sources: Bloomberg, Morningstar, Robert Shiller, Elroy Dimson, Paul Marsh and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press, 2002; Elroy Dimson, Paul Marsh and Mike Staunton, Credit Suisse Global Returns Yearbook and Sourcebook, 2018, Zurich: Credit Suisse Research Institute, 2021
Assessing expected returns is a challenging, but necessary, exercise for portfolio managers and financial planners. While assessing reasonable (and hopefully useful) estimates for expected returns is difficult, it is likely even more difficult for investors to capture them in live portfolios. The expected return is a concept that can be difficult for investors to grasp because returns are very volatile over short periods, and periods of low realized returns are often associated with higher expected returns. It is easy for investors to get discouraged and abandon their investment plan during periods of disappointing realized returns, which may, in hindsight, be the worst times to do so.
The cognitive and behavioral errors of investors are well-documented – see, for example Barber & Odean (2013). Many investors may benefit from a professional financial advisor to manage their portfolio in a disciplined way, avoiding the distractions brought by market fluctuations and new products that promise the moon. However, finding the right advisor is critical, as many advisors are prone to the same errors as investors, and in some samples such as Linnainmaa et al. (2021), to an even greater extent than the clients that they serve.
[1] We have also launched a document for factor-tiled portfolios, with different expected returns, standard deviations and correlations.
