High-profile financial disasters have been linked to risks being less diversified than expected. Some of these involve financial agents acting on behalf of source-investors. Such a financial-agent network can be found in the venture capital sector. It has been understood that the institutional funds that invest in Venture Capital firms ("VCs") can diversify their financial portfolio risk by investing in several VCs. But the adverse scenario remains that an institutional fund invests in more than one VC, which chooses, via syndication, to invest in the same venture. This creates less diversification than expected. The result is inadvertent systemic risk for the institutional fund. A random sampling model is developed to explore this network scenario; encompassing both the source and destination of VCs' funds. The study uses a data set of 20 UK-based VCs and 73 institutional funds, making a total of 218 investments in VCs, in the period 1993-2003. The findings reject the view that institutional funds investing in multiple VCs tend to do so such that risk is minimised via diversification; the observed pattern of relationships is worse-than-random. Risk in investment networks can be materially higher than any standard portfolio analysis would show.