The monthly return of your portfolio is 3%. What is the probability of realizing a 1% return on a given month<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the probability of realizing a 1% return on a given month when the expected monthly return of your portfolio is 3%, more information about the return distribution is needed. Typically, financial returns are modeled as normally distributed random variables. The expected return (mean) is 3%, but the probability of getting exactly 1% depends on the standard deviation (volatility) of returns.<\/p>\n\n\n\n If the returns follow a normal distribution with mean \u03bc=3%\\mu = 3\\% and standard deviation \u03c3\\sigma, the probability of exactly 1% return is zero because the probability of any single point in a continuous distribution is zero. Instead, we consider the probability of returns falling within an interval around 1%, for example between 0.5% and 1.5%.<\/p>\n\n\n\n To calculate this, we standardize the return using the Z-score formula: Z=X\u2212\u03bc\u03c3Z = \\frac{X – \\mu}{\\sigma}<\/p>\n\n\n\n where XX is the target return (1%). Using this, the probability of observing a return near 1% is the area under the normal curve between the Z-scores corresponding to the chosen interval.<\/p>\n\n\n\n Without the standard deviation, the exact probability cannot be computed. If the standard deviation is known, the steps are:<\/p>\n\n\n\n In practice, portfolio returns fluctuate around the mean 3% with some variability. A 1% return is less than the average return, so the probability will depend on how spread out returns are. A low standard deviation means returns cluster near 3%, making a 1% return less likely. A high standard deviation means returns vary widely, making a 1% return more likely.<\/p>\n\n\n\n In summary, the probability of realizing exactly 1% return in a month cannot be stated without knowing the return volatility or distribution shape. With a normal distribution assumption and known standard deviation, the probability can be found by standardizing the target return and looking up cumulative probabilities<\/p>\n","protected":false},"excerpt":{"rendered":" The monthly return of your portfolio is 3%. What is the probability of realizing a 1% return on a given month The correct answer and explanation is: To find the probability of realizing a 1% return on a given month when the expected monthly return of your portfolio is 3%, more information about the return […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37938","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37938"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37938\/revisions"}],"predecessor-version":[{"id":37939,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37938\/revisions\/37939"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n