Question in diversification benefits from currency exposure

Hi, everyone. I am reading the topic of Currency Management Rd.19.Particularly, in 4.3.1 Diversification Considerations, the textbook says:" correlation between foreign-currency returns and foreign-currency asset returns tends to be greater for fixed-income portfolios than for equity portfolios. This assertion makes intuitive sense: both bonds and currencies react strongly to movements in interest rates, whereas equities respond more to expected earnings. As a result, the implication is that currency exposures provide little diversification benefit to fixed-income portfolios and that the currency risk should be hedged"

(Institute 390)

Institute, CFA. 2018 CFA Program Level III Volume 3 Applications of Economic Analysis and Asset Allocation. CFA Institute, 07/2017. VitalBook file.

But my consideration is that correlation between bonds and currency is somehow negative if we assume that interest rate is their only common factor. Since rising interest would cause bond price goes down and thus falling return but currency would be stronger and increasing return, the correlation is apparently negative. Therefore, currency exposure does provide diversification benefits.

Can anyone share ideas or point out my mistakes?

Add an inflation variable into this assumption and probably consequence would be that currency as well as bond value in that currency would lose in value in the scenario of rising foreign IR significantly measured in domestic currency units.

Got you. Thanks buddy!