# TOD Index: Low correlation to FTSE Nareit U.S. Real Estate Index, implying diversification benefit to investors

Numerous academic studies have shown that investors who diversify their portfolios may increase an investor’s increase long-term portfolio returns without taking on additional risk. Diversification can potentially reduce portfolio volatility and mitigate losses from any one security or asset class.

More specifically, Modern portfolio theory (MPT) emphasizes that investors can diversify away the risk of investment loss by reducing the correlation between the returns from the select securities in their portfolio. Harry Markowitz, winner of the Nobel Prize in Economics, put it succinctly "To reduce risk, it is necessary to avoid a portfolio whose securities are all highly correlated with each other." (Markowitz, 1991).

Correlation is the tendency for the returns of two assets, in this case, the TOD Price Index and the FTSE Nareit U.S. Real Estate Index Series , to move together relative to their average, although it does not necessarily show that one causes the other to change.

The measurement of this statistic (the correlation coefficient) can range from -1 (perfect negative correlation, one goes up, the other down) to +1 (perfect positive correlation. A correlation coefficient of zero means that two variables do not have a correlational association of any kind.

MPT stresses that investors should look for a consistently uncorrelated (near zero) pool of assets to limit risk. The rolling 15 year correlation of the TOD Price Index to the FTSE Nareit U.S. Real Estate Index Series is .036, a very low correlation.

In other words, the TOD price index returns have tended to zig while the returns of publicly traded REITs have tended to zag. Thus, TOD Price Index can be used to potentially help investors diversify a real estate portfolio.

*Correlation is a critical metric that can provide useful information in the portfolio construction process. Nevertheless, it is important for investors to understand that correlation is a property of random variables, and so does not describe a fixed relationship between variables: Assets with low and unchanging correlation can and do move in the same direction from time to time. In addition, correlations between and among asset class returns can and do change over time or in particular circumstances. Future correlations may also differ from those in the past because of changing economic and market regimes. Investors should take these factors into consideration when using correlation as a key input for constructing investment portfolios and not rely solely on statistical measures.*

### TOD Index – A historical ability to capture outsized gains in rising markets and to minimize losses in declining markets: The Upside and Downside Capture Ratios

The Upside and Downside capture ratios are a tool to determine whether a strategy historically performed better or worse than a benchmark in rising and in falling markets and by how much.Investors utilize these ratios to ideally identify which strategies may potentially generate outsized returns in the future when the benchmark rises, and which strategies may hypothetically result in smaller losses when the benchmark declines, in this case, the TOD Price Index relative to the Zillow National Average Home Values Returns.

The Capture Ratios are separated into two groups: up capture, when the benchmark rises, and down capture, when the benchmark falls.

Upside capture ratio measures the percentage of the gains captured by a strategy when the benchmark is up.

Upside capture ratios are calculated by taking the strategy's monthly return during months when the benchmark had a positive return and dividing it by the benchmark return during that same month.

The upside capture ratio should ideally be greater than 100%, which would indicate that during periods when the benchmark is up, the strategy generally outperformed during periods of positive returns for the benchmark.

For example, if the average up return for the TOD Price Index was 12% and the average up return for Zillow National Average Home Values Returns was 10%, then the upside capture ratio would be 120%, indicating the TOD Price Index rose 20% greater than the benchmark in prior up markets. The higher the upside capture ratio, the better.

If a strategy’s increase is the same as the benchmark, the strategy’s upside capture ratio is 100%, for example, if the average up return for both the TOD Price Index and Zillow National Average Home Values Returns was 5%.

Downsize capture ratio measures the percentage of market losses endured by a strategy when the benchmark is down.

Downside capture ratios are calculated by taking the strategy's monthly return during the periods of negative benchmark performance and dividing it by the benchmark return.

The down capture ratio should ideally be less than 100%, which would indicate that during periods when the benchmark is down, the strategy has generally outperformed during periods of negative returns for the benchmark.

For example, if the average down return for the TOD Price Index was down 7% and the average down return for Zillow National Average Home Values Returns was 10%, then the upside capture ratio would be, 70% indicating the TOD Price Index lost 30% less than the benchmark in prior down markets. The lower the downside capture ratio, the better.

The goal is to find strategies that have a high upside capture ratio, but a low or negative downside capture ratio.

Applied to the TOD Index, the TOD Price Index historically captured 132% of the gains in the Zillow National Average Home Values Returns when the latter was up. The historical downside capture ratio is 32%, indicating the TOD Price Index sustained only 32% of the losses in the Zillow National Average Home Values Returns when the benchmark was down, reflecting an attractive asymmetry.

Legend

The graph above represents the upside and downside capture ratios.

The reference point is the benchmark, the Zillow National Average Home Values Returns, as noted by the crosshairs in the middle.

The upper left quadrant represents the ideal location for a strategy. Here the TOD Price Index is historically up more than the benchmark in up periods and down less in declining periods, an attractive asymmetry.

The lower left quadrant represents a strategy that rises less than the benchmark and declines less when the benchmark declines, indicating a more conservative strategy.

The top right quadrant represents an aggressive strategy that both rises more than the benchmark when the latter rises and declines more when the benchmark declines.

The lower left is the least attractive quadrant indicating a strategy that is historically up less than the benchmark in up periods and down more in declining periods.

Disclaimer

*The TOD Price Index is an index, and it is not possible to invest directly in an index. Index performance does not reflect the deduction of any fees or expenses. Any indices and other financial benchmarks are provided for illustrative purposes only. All investments are subject to risk. Past performance is no guarantee of future results. The performance of an index is not an exact representation of any particular investment, as you cannot invest directly in an index.*