## Treynor Ratios: Joint Venture Cash Flow Distribution & Fairness Quantified

**By Zachary Shipps**

**NAREIM Fellow, MIT MSRED ’14**

*Twice a year, NAREIM invites graduate students from the top real estate programs across the country to attend our Executive Officers’ Meetings as Fellows. **After attending the September EO Meeting, Zachary Shipps, a 2014 MSRED candidate at MIT concentrating in Real Estate Finance, considered how rigor may be applied how JV partnerships are negotiated as they move beyond their traditional definitions.** *

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The distribution clauses of most joint venture agreements have long been negotiated without the rigor of a benchmark more sophisticated than a prior deal, a panel from the latest conference, or attorney’s opinions about what they can get for their clients without serious consideration of how the capital markets are pricing risk expected returns. The following approach enables users to compute a benchmark for quantifying the fairness of risk-adjusted returns in joint venture agreements as a robust compliment to employing long-standing practices in JV negotiations. Though market and capital fluctuations ultimately determine the structure of the joint venture construction, the Treynor ratio method, taught by Professor Dr. David Geltner to graduate students at the MIT Center for Real Estate, provides a rigorous level of understanding on where parties land in regards to risk expected returns which can be leveraged in negotiating JV agreements.

The method suggests an assessable approach that is based on classical financial principles and evidence from the capital markets to apply a more rigorous framework for judging the fairness of joint venture distributions by comparing the Risk Premium to Risk Ratio, otherwise known as the Treynor Ratio, of both JV partners.

This understanding enables users to compare capital or operating partners as well as investment opportunities from a standardized approach. This deeper analysis will result in more accurate investment decisions being made by defining the risk as a better-known quantity. Additionally, a clearer understanding of the risk will impact the negotiation of other important components of the JV agreement such as timing and control, which have a direct impact on the profitability for both sides of the partnership. With a negligible amount of additional analysis, users will realize an edge over competition through a uniform framework with which to judge joint venture investments, provide a more astute understanding of the risk of an investment in relation to the market, and leverage in the negotiating the agreement to their best position possible.

In classical capital markets theory, the Security Market Line (SML) graphs the expected return versus the risk incurred for a specific investment. The x-axis of the SML represents the investment risk and the y-axis represents the expected return of the investment. The horizontal axis can be approached as reflecting investment risk in regards to how the market perceives such risk as shown in observable traded asset prices. In classical theory such risk may be represented by the asset’s beta, but this scenario need not be restricted to such a specific metric as in this context the *relative* risk difference between the two parties is of sole importance for consideration.

The Risk Free rate is generally derived based on Treasury yields, represented by a dashed line in the following Exhibits. The capital markets determine the slope of the Security Market Line as the price of risk, where the expected return increases with each additional unit of risk.

If the prospective investment falls on the Security Market Line, the return is considered to be fairly adjusted for the risk incurred given the market price of risk and the risk-free rate. An investment that plots above the SML would be viewed as undervalued, as the investor can expect a higher return for the risk taken, whereas an investment below the SML would be considered overvalued because the investor would be accepting a lower return for the risk taken.

**Exhibit 1**

In an asset priced at the fair market value, all investment points will lie along the Security Market Line including the debt, project, and joint venture agreement. Any investments in the project should receive an equitable proportion of risk for the return gained, and conversely should receive an equitable increment to their going-in return risk premium so as to reflect the risk exposure.

### **Exhibit 2**

The Treynor Ratio is the ratio of the Risk Premium divided by the Risk of an investment and the slope of which is represented by the dashed line on Exhibit 3.

**Exhibit 3**

In order to measure the relative risk specified in the denominator of the Treynor Ratio, the simplest approach is to model a binomial future scenario to quantify the risk faced by each partner. The Treynor Ratio is calculated using the Internal Rate of Return (IRR) metric represented by each partner. The expected return necessary in the numerator of the Ratio is modeled by a base case that reflects the most likely outcome for the project. The risk necessary in the denominator of the Ratio is quantified as the range of IRR outcomes between two scenarios, a pessimistic and an optimistic case for the performance of the asset. The optimistic and pessimistic scenarios may be thought of as reflecting a 10% chance of occurring. The Risk of the investment is defined as the ex post IRR range between the pessimistic and optimistic cases and is derived by subtracting the downside case from the upside case as outlined in Exhibit 4.

Optimistic Scenario^{1}: Defined as the Base Case altered as follows

25% *Higher* initial revenue projections (Rent/SF, Exit Price, Other Revenue)

2% *Faster* growth in revenues over time

Pessimistic Scenario[1]: Defined as the Base Case altered as follows

25% *Lower* initial revenue projections (Rent/SF, Exit Price, Other Revenue)

2% *Slower* growth in revenues over time

The numerator of the Treynor Ratio, or Risk Premium, is calculated by subtracting the Risk Free Rate, commonly based on Government bond yields, from the Base Case scenario. The Ratio is then computed for each partner. What matters for judging the fairness of the agreement terms from this perspective is specifically only the *ratio of these ratios* as shown in Exhibit 4. This enables the exact nature of the risk metric to cancel out, as long as the range of optimistic less pessimistic IRR outcomes reflects the *relative* amount of risk each party faces.

*Treynor Rati0 = Base Case – Risk Free Rate / Optimistic Case – (Pessistimsitci Case)*

- Assumed Risk Free Rate = 2.5% (10 Year U.S. Treasury)
- Returns calculated using a levered Internal Rate of Return

**Exhibit 4**

These representative Treynor Ratios are very similar despite the variance in returns to each partner as represented in Exhibit 5. Thus, in this case, the analysis suggests a fair and equitable risk adjusted return for each party. A difference of less than 10% between the two parties’ ratios is considered to be within the bounds of fairness and estimation error.

**Exhibit 5**

Important variables to consider when calculating Treynor Ratios include development and acquisition fees to the operating partner, which may not completely cover costs. Additionally, control components in the JV that enhance or decrease one party’s risk may be impossible to fully quantify and are not represented in the Treynor Ratio. In a development scenario, the point at which the capital partner is introduced to the project in relation to the entitlement process will also need to be contemplated as it has a direct effect on the risk components of the deal.

While not an exhaustively conclusive analysis of the fairness of joint venture cash flow distribution terms, this type of Treynor Ratio based analysis begins to bring some depth and rigor into consideration to improve the efficiency of joint venture agreements. Though market timing and capital fluctuations ultimately determine the structure of joint venture agreements, firms, which leverage the Treynor Ratio as part of their analysis, will realize an edge over competition. Employing the Treynor Ratio will result in better understanding the risk in correlation with the return of an investment, more efficiently judging joint venture opportunities through a standardized framework, and ultimately negotiating a better position in the joint venture agreement.

[1] Using scenarios 25% Higher and 25% Lower than the calculated Base Case scenario result in IRR’s near the 10^{th} and 90^{th} percentile in outcome probabilities based on empirically calibrated modeling of typical real estate risk (volatility, trends, cycles, noise) based on actual empirical evidence from a large sample of U.S. property investments, such as transaction price indexes from firms such as Real Capital Analytics, Inc.