This paper explores the question in which market phases arbitrage between listed real estate companies and non-listed real estate funds is possible for institutional investors.

The term arbitrage implies the skimming of profits by exploiting price differences of assets in different markets. Applied to listed and unlisted real estate portfolios, this describes the fact that profits can be made by converting listed real estate portfolios into unlisted ones and vice versa. Arbitrage between listed and unlisted real estate portfolios is basically possible in two ways:

• Firstly, through a de-listing or conversion of a listed real estate company to a real estate special fund;
• Secondly, through a listing or IPO or spin-off of a special real estate fund to a listed real estate company.

For this purpose, the total return time series of listed and non-listed stocks in the same period are compared in each case. The FTSE EPRA NAREIT Developed Europe Office Index was used as the total return time series for listed European real estate companies and INREV data of special real estate funds with a comparable regional and sectoral investment focus as the total return time series for non-listed holdings. The period under review covers the periods from Q1 2007 to Q3 2018.

In doing so, the authors examine the data series for both non-risk-adjusted and risk-adjusted arbitrage. The risk-adjusted analysis is carried out using a modified Sharpe ratio, based on the one hand on a forecasted arbitrage time series and on the other hand on an arbitrage time series supplemented by a (supposedly) risk-free investment alternative. Both predicted arbitrage time series are set in relation to the "more" risk as the difference from the respective dispersions. In this context, only the forecasted arbitrage time series or the forecasted arbitrage time series supplemented by a (supposedly) risk-free investment alternative are responsible for the positive or negative characteristics of the modified Sharpe ratios, since the risk of EPRA is always above the risk of INREV.

For analytical reasons, this study deliberately abstracts from legal and operational restrictions and transaction costs of the respective conversion.

It can be seen that negative modified Sharpe ratios exist in three time periods - in these time periods, arbitrage against listed real estate companies can therefore be expected through investments in real estate special funds or through de-listing or conversion of listed real estate companies to real estate special funds.

Conversely, positive modified Sharpe ratios can also be identified in three periods - in these periods, arbitrage against listed real estate special funds can therefore be expected through investments in listed real estate companies or through listing or IPO or spin-off of real estate special funds to listed real estate companies.