Answer:
Value at Risk is used to measure just how much is expected to be lost resulting from an investment over a period of time.
Standard Deviation is used to measure the risk of volatility in the returns of investments. It can measure idiosyncratic risk which is the risk inherent in an investment.
A. You buy life insurance. Value At risk.
Insurance has to do with Value at Risk to measure how much would have to be paid out.
B. You hire an investment advisor who specializes in international diversification in stock portfolios. Standard Deviation.
Diversification is based on the risk of stock volatility and is done to reduce idiosyncratic risk so this has to do with Standard deviation.
C. In your role as a central banker, you provide emergency loans to illiquid intermediaries. Value At Risk.
These illiquid intermediaries might be unable to pay back so the assessment needs to find out how much could potentially be lost.
D. You open a kiosk at the mall selling ice cream and hot chocolate. Standard Deviation.
These products will be sold in alternating seasons to ensure profitability is maintained. The idiosyncratic risk of selling only one of these was therefore targeted making this an example of Standard Deviation based risk assessment.