A Bundesbank paper proposes a new type of real exchange rate index. Rather than measuring the competitiveness of goods markets, this “real financial exchange rate” would measure the competitiveness of asset markets. There is some evidence that this indicator helps detecting overvaluation.

Real financial market exchange rates and capital flows”, Maria Gelman, Axel Jochem and Stefan Reitz.
Deutsche Bundesbank, Discussion Paper, No 50/2013
http://econstor.eu/bitstream/10419/88439/1/774080795.pdf

The below are excerpts from the paper. Emphasis and cursive text has been added.

The idea behind real financial exchange rates

“The importance of international capital transactions has increased, and their value meanwhile far exceeds that of cross-border goods market transactions. This suggests that it would be appropriate to construct real exchange rates based not only on goods market equilibriums [conventional real effective exchange rates] but also on capital market equilibriums… the suggested index can be viewed as the price competitiveness of a country’s assets.”

N.B: “The [conventional] real effective exchange rate (REER) is a pivotal variable in the open economy macroeconomics. With the expansion in trade in goods and services, the REER has emerged as a prime indicator of price competitiveness of economies in the economic policy arena. With its roots in the law of one price on integrated international goods markets, REER’s theoretical concepts, empirical applications and its impact on countries’ output and wealth have been extensively studied.”

The calculation of real financial exchanges rates

“We construct an index of real effective financial exchange rates [REFER] as a weighted average of cross-country asset price ratios…The underlying idea is to construct effective financial market exchange rates as an indicator of the relative attractiveness of different countries’ assets. It emerges that the indicators of price competitiveness on the goods markets on the one hand and the corresponding financial market indicators on the other may diverge considerably at times. Consequently, they may well provide different information.”

“A panel of 15 leading stock markets [for the period 1993-2011] is used to construct and empirically investigate the index of real effective financial market exchange rates. While at the first stage, nominal bilateral exchange rates are deflated by MSCI stock market indices to obtain real bilateral financial market exchange rates, weights based on bilateral cross-holdings of equity securities…are used to calculate the REFER as a geometric average of bilateral values at the second stage. By doing so our indicator reflects the relative attractiveness of a country’s financial assets as compared to its capital market competitors in the same way as we interpret standard real effective exchange rates based on goods market prices.”

The information value of real financial exchange rates

“A co-integration analysis [statistical analysis of the relation between non-stationary time series, i.e. series that have a long-term drift] examines the correlation of the real effective financial market exchange rate with net foreign holdings of domestic shares relative to domestic stock market capitalisation. The estimates demonstrate a significant positive correlation…Temporary deviations of the effective financial market exchange rate from its path predicted by fundamentals give hints to possible over- or undervaluation of asset prices.”

“Error correction analysis [analysis of how deviations of two co-integrated series affect these series’ future dynamics] reveals that both, the real financial market exchange rate and international capital flows adjust to restore the long-run equilibrium…In case of a positive deviation from the long-run equilibrium, implying that the current REFER is higher than its equilibrium value, a depreciation of the real effective financial exchange rate proportional to the current error can be expected to restore equilibrium.”

“We also find a significant reaction of net foreign holdings to a given deviation from the long-run equilibrium. Here, a positive error is followed by capital flows into the appreciating currency. Obviously, a higher valuation of a country’s assets as measured by the real effective financial exchange rate induces foreign investors to reallocate their portfolios at the benefit of domestic securities. This implies that a fraction of the observed change of the real exchange rate is perceived to be permanent…[Likewise] an excess world holding of a country’s assets (in terms of the relative price of the country’s assets) is corrected by subsequent capital outflows.”

“This is in contrast to the real effective exchange rates based on goods market prices, where the deviation from the long-run equilibrium fails to predict capital flows.”